%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n012.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 17:43:01 EDT 2023

% Result   : Theorem 22.40s 3.76s
% Output   : Proof 28.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n012.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 23 13:46:12 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 0.21/0.66  ________       _____
% 0.21/0.66  ___  __ \_________(_)________________________________
% 0.21/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66  
% 0.21/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66  (2023-06-19)
% 0.21/0.66  
% 0.21/0.66  (c) Philipp Rümmer, 2009-2023
% 0.21/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66                Amanda Stjerna.
% 0.21/0.66  Free software under BSD-3-Clause.
% 0.21/0.66  
% 0.21/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66  
% 0.21/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.67  Running up to 7 provers in parallel.
% 0.21/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 4.49/1.35  Prover 4: Preprocessing ...
% 4.49/1.35  Prover 1: Preprocessing ...
% 4.49/1.38  Prover 5: Preprocessing ...
% 4.49/1.38  Prover 6: Preprocessing ...
% 4.49/1.38  Prover 0: Preprocessing ...
% 4.49/1.38  Prover 2: Preprocessing ...
% 4.49/1.38  Prover 3: Preprocessing ...
% 11.46/2.28  Prover 1: Warning: ignoring some quantifiers
% 11.46/2.29  Prover 5: Proving ...
% 11.79/2.32  Prover 6: Proving ...
% 11.79/2.36  Prover 3: Warning: ignoring some quantifiers
% 11.79/2.36  Prover 1: Constructing countermodel ...
% 11.79/2.38  Prover 4: Warning: ignoring some quantifiers
% 11.79/2.39  Prover 3: Constructing countermodel ...
% 11.79/2.40  Prover 2: Proving ...
% 12.54/2.47  Prover 4: Constructing countermodel ...
% 13.10/2.54  Prover 0: Proving ...
% 22.40/3.76  Prover 0: proved (3076ms)
% 22.40/3.76  
% 22.40/3.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.40/3.76  
% 22.40/3.76  Prover 3: stopped
% 22.40/3.76  Prover 2: stopped
% 22.40/3.76  Prover 5: stopped
% 22.40/3.76  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.40/3.76  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.40/3.76  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.40/3.76  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.79/3.77  Prover 6: stopped
% 22.79/3.77  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.63/3.90  Prover 7: Preprocessing ...
% 23.63/3.92  Prover 8: Preprocessing ...
% 24.02/3.93  Prover 11: Preprocessing ...
% 24.17/3.95  Prover 13: Preprocessing ...
% 24.17/3.96  Prover 10: Preprocessing ...
% 25.40/4.16  Prover 10: Warning: ignoring some quantifiers
% 25.40/4.19  Prover 8: Warning: ignoring some quantifiers
% 26.03/4.20  Prover 7: Warning: ignoring some quantifiers
% 26.03/4.20  Prover 13: Warning: ignoring some quantifiers
% 26.03/4.21  Prover 10: Constructing countermodel ...
% 26.03/4.22  Prover 8: Constructing countermodel ...
% 26.03/4.22  Prover 7: Constructing countermodel ...
% 26.03/4.23  Prover 13: Constructing countermodel ...
% 27.06/4.39  Prover 11: Warning: ignoring some quantifiers
% 27.06/4.39  Prover 1: Found proof (size 375)
% 27.06/4.40  Prover 1: proved (3702ms)
% 27.06/4.40  Prover 4: stopped
% 27.06/4.40  Prover 10: stopped
% 27.06/4.40  Prover 7: stopped
% 27.06/4.40  Prover 13: stopped
% 27.06/4.40  Prover 8: stopped
% 27.06/4.42  Prover 11: Constructing countermodel ...
% 27.72/4.43  Prover 11: stopped
% 27.72/4.43  
% 27.72/4.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.72/4.43  
% 27.72/4.47  % SZS output start Proof for theBenchmark
% 27.72/4.48  Assumptions after simplification:
% 27.72/4.48  ---------------------------------
% 27.72/4.48  
% 27.72/4.48    (d10_xboole_0)
% 28.03/4.50     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ~ $i(v1) | 
% 28.03/4.50      ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0: $i]
% 28.03/4.50    :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, v0) = v1) |  ~ $i(v0))
% 28.03/4.50  
% 28.03/4.50    (d1_zfmisc_1)
% 28.03/4.51     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (powerset(v1) = v2) | 
% 28.03/4.51      ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] :
% 28.03/4.51      (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) |  ~ (v4 =
% 28.03/4.51            0)) & (v5 = 0 | v4 = 0))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 28.03/4.51      (powerset(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v2: $i] :  ! [v3: int] :
% 28.03/4.51        (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ $i(v2) |  ? [v4: int] : ( ~ (v4 =
% 28.03/4.51              0) & in(v2, v1) = v4)) &  ! [v2: $i] : ( ~ (subset(v2, v0) = 0) |  ~
% 28.03/4.51          $i(v2) | in(v2, v1) = 0)))
% 28.03/4.51  
% 28.03/4.51    (d2_subset_1)
% 28.03/4.51     ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (element(v1, v0) = v2) |  ~
% 28.03/4.51      $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (empty(v1) = v4 &
% 28.03/4.51        empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) |
% 28.03/4.51              v4 = 0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~
% 28.03/4.51      (element(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any]
% 28.03/4.51      : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & (
% 28.03/4.51              ~ (v2 = 0) | v4 = 0)))))
% 28.03/4.51  
% 28.03/4.51    (d3_tarski)
% 28.03/4.51     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 28.03/4.51      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 28.03/4.51          v1) = v4 & in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 28.03/4.51      (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~ (in(v2, v0)
% 28.03/4.51          = 0) |  ~ $i(v2) | in(v2, v1) = 0))
% 28.03/4.51  
% 28.03/4.51    (d4_tarski)
% 28.03/4.51     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (union(v1) = v2) |  ~
% 28.03/4.51      $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] : (in(v3, v0) = v4 & $i(v3)
% 28.03/4.51        & ( ~ (v4 = 0) |  ! [v5: $i] : ( ~ (in(v3, v5) = 0) |  ~ $i(v5) |  ? [v6:
% 28.03/4.51              int] : ( ~ (v6 = 0) & in(v5, v1) = v6))) & (v4 = 0 |  ? [v5: $i] :
% 28.03/4.51          (in(v5, v1) = 0 & in(v3, v5) = 0 & $i(v5))))) &  ! [v0: $i] :  ! [v1:
% 28.03/4.51      $i] : ( ~ (union(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v2: $i] :  ! [v3:
% 28.03/4.51          int] : (v3 = 0 |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ! [v4: $i] : ( ~
% 28.03/4.51            (in(v2, v4) = 0) |  ~ $i(v4) |  ? [v5: int] : ( ~ (v5 = 0) & in(v4,
% 28.03/4.51                v0) = v5))) &  ! [v2: $i] : ( ~ (in(v2, v1) = 0) |  ~ $i(v2) |  ?
% 28.03/4.51          [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3)))))
% 28.03/4.51  
% 28.03/4.51    (d4_xboole_0)
% 28.03/4.52     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~
% 28.03/4.52      (set_difference(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 28.03/4.52        $i] :  ? [v5: any] :  ? [v6: any] :  ? [v7: any] : (in(v4, v2) = v7 &
% 28.03/4.52        in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) |  ~ (v5 = 0) |
% 28.03/4.52          v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0))))) &  ! [v0: $i] :  ! [v1:
% 28.03/4.52      $i] :  ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |  ~ $i(v2) |  ~
% 28.03/4.52      $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4: any] : ( ~ (in(v3, v0) = v4) | 
% 28.03/4.52          ~ $i(v3) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) =
% 28.03/4.52            v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0))))) &  ! [v3: $i] : ( ~
% 28.03/4.52          (in(v3, v0) = 0) |  ~ $i(v3) |  ? [v4: any] :  ? [v5: any] : (in(v3, v2)
% 28.03/4.52            = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 28.03/4.52  
% 28.03/4.52    (d5_subset_1)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (element(v1, v2) = 0) |  ~
% 28.03/4.52      (powerset(v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :
% 28.03/4.52      (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & $i(v3)))
% 28.03/4.52  
% 28.03/4.52    (fc1_subset_1)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) |  ? [v2: int]
% 28.03/4.52      : ( ~ (v2 = 0) & empty(v1) = v2))
% 28.03/4.52  
% 28.03/4.52    (involutiveness_k3_subset_1)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v1 |  ~
% 28.03/4.52      (subset_complement(v0, v2) = v3) |  ~ (subset_complement(v0, v1) = v2) |  ~
% 28.03/4.52      $i(v1) |  ~ $i(v0) |  ? [v4: $i] :  ? [v5: int] : ( ~ (v5 = 0) & element(v1,
% 28.03/4.52          v4) = v5 & powerset(v0) = v4 & $i(v4)))
% 28.03/4.52  
% 28.03/4.52    (l32_xboole_1)
% 28.03/4.52    $i(empty_set) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = empty_set |  ~
% 28.03/4.52      (set_difference(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~
% 28.03/4.52        (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 28.03/4.52      (set_difference(v0, v1) = empty_set) |  ~ $i(v1) |  ~ $i(v0) | subset(v0,
% 28.03/4.52        v1) = 0)
% 28.03/4.52  
% 28.03/4.52    (rc1_subset_1)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) | empty(v0) =
% 28.03/4.52      0 |  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) & element(v2, v1) = 0 &
% 28.03/4.52        empty(v2) = v3 & $i(v2)))
% 28.03/4.52  
% 28.03/4.52    (rc1_xboole_0)
% 28.03/4.52     ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 28.03/4.52  
% 28.03/4.52    (rc2_subset_1)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) |  ? [v2: $i]
% 28.03/4.52      : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2)))
% 28.03/4.52  
% 28.03/4.52    (symmetry_r1_xboole_0)
% 28.03/4.52     ! [v0: $i] :  ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)
% 28.03/4.52      | disjoint(v1, v0) = 0)
% 28.03/4.52  
% 28.03/4.52    (t1_zfmisc_1)
% 28.03/4.52    $i(empty_set) &  ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 28.03/4.52      = v0 & $i(v0))
% 28.03/4.52  
% 28.03/4.52    (t2_xboole_1)
% 28.03/4.52    $i(empty_set) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(empty_set,
% 28.03/4.52          v0) = v1) |  ~ $i(v0))
% 28.03/4.52  
% 28.03/4.52    (t37_xboole_1)
% 28.03/4.52    $i(empty_set) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = empty_set |  ~
% 28.03/4.52      (set_difference(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~
% 28.03/4.52        (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 28.03/4.52      (set_difference(v0, v1) = empty_set) |  ~ $i(v1) |  ~ $i(v0) | subset(v0,
% 28.03/4.52        v1) = 0)
% 28.03/4.52  
% 28.03/4.52    (t3_boole)
% 28.03/4.52    $i(empty_set) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (set_difference(v0,
% 28.03/4.52          empty_set) = v1) |  ~ $i(v0))
% 28.03/4.52  
% 28.03/4.52    (t3_xboole_1)
% 28.03/4.53    $i(empty_set) &  ! [v0: $i] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0)
% 28.03/4.53      |  ~ $i(v0))
% 28.03/4.53  
% 28.03/4.53    (t43_subset_1)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (element(v1, v2) = 0) |  ~
% 28.03/4.53      (powerset(v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ! [v3: $i] : ( ~ (element(v3,
% 28.03/4.53            v2) = 0) |  ~ $i(v3) |  ? [v4: any] :  ? [v5: $i] :  ? [v6: any] :
% 28.03/4.53        (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) =
% 28.03/4.53          v6 & $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))))
% 28.03/4.53  
% 28.03/4.53    (t48_xboole_1)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 28.03/4.53      (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) |  ~ $i(v1)
% 28.03/4.53      |  ~ $i(v0) | (set_intersection2(v0, v1) = v3 & $i(v3)))
% 28.03/4.53  
% 28.03/4.53    (t4_xboole_0)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 28.03/4.53      |  ~ $i(v1) |  ~ $i(v0) | disjoint(v0, v1) = 0 |  ? [v3: $i] : (in(v3, v2) =
% 28.03/4.53        0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 28.03/4.53      (set_intersection2(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : (
% 28.03/4.53        ~ (v3 = 0) & disjoint(v0, v1) = v3) |  ! [v3: $i] : ( ~ (in(v3, v2) = 0) |
% 28.03/4.53         ~ $i(v3)))
% 28.03/4.53  
% 28.03/4.53    (t50_subset_1)
% 28.03/4.53    $i(empty_set) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (v0 = empty_set) &
% 28.03/4.53      powerset(v0) = v1 & $i(v1) & $i(v0) &  ? [v2: $i] :  ? [v3: $i] :
% 28.03/4.53      (subset_complement(v0, v2) = v3 & element(v2, v1) = 0 & $i(v3) & $i(v2) &  ?
% 28.03/4.53        [v4: $i] :  ? [v5: int] :  ? [v6: int] : ( ~ (v6 = 0) &  ~ (v5 = 0) &
% 28.03/4.53          element(v4, v0) = 0 & in(v4, v3) = v6 & in(v4, v2) = v5 & $i(v4))))
% 28.03/4.53  
% 28.03/4.53    (t6_boole)
% 28.03/4.53    $i(empty_set) &  ! [v0: $i] : (v0 = empty_set |  ~ (empty(v0) = 0) |  ~
% 28.03/4.53      $i(v0))
% 28.03/4.53  
% 28.03/4.53    (t83_xboole_1)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (disjoint(v0, v1) =
% 28.03/4.53        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] : ( ~ (v3 = v0) &
% 28.03/4.53        set_difference(v0, v1) = v3 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 28.03/4.53      (disjoint(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | set_difference(v0, v1) =
% 28.03/4.53      v0)
% 28.03/4.53  
% 28.03/4.53    (t8_boole)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)
% 28.03/4.53      |  ~ $i(v1) |  ~ $i(v0))
% 28.03/4.53  
% 28.03/4.53    (t99_zfmisc_1)
% 28.03/4.53     ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) | union(v1) =
% 28.03/4.53      v0)
% 28.03/4.53  
% 28.03/4.53    (function-axioms)
% 28.03/4.54     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 28.03/4.54    [v3: $i] : (v1 = v0 |  ~ (are_equipotent(v3, v2) = v1) |  ~
% 28.03/4.54      (are_equipotent(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 28.03/4.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (disjoint(v3,
% 28.03/4.54          v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 28.03/4.54    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (subset_complement(v3, v2) = v1) |  ~
% 28.03/4.54      (subset_complement(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 28.03/4.54    :  ! [v3: $i] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~
% 28.03/4.54      (set_difference(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 28.03/4.54    ! [v3: $i] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~
% 28.03/4.54      (cartesian_product2(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 28.03/4.54    :  ! [v3: $i] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~
% 28.03/4.54      (ordered_pair(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 28.03/4.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (element(v3,
% 28.03/4.54          v2) = v1) |  ~ (element(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 28.03/4.54    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 28.03/4.54      (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 28.03/4.54      $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (set_intersection2(v3, v2) =
% 28.03/4.54        v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 28.03/4.54    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~
% 28.03/4.54      (set_union2(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 28.03/4.54    [v3: $i] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~
% 28.03/4.54      (unordered_pair(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 28.03/4.54      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 28.03/4.54      (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0)) &  ! [v0:
% 28.03/4.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 28.03/4.54    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0: $i] :  !
% 28.03/4.54    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0))
% 28.03/4.54    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1
% 28.03/4.54      = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0: $i] :  ! [v1:
% 28.03/4.54      $i] :  ! [v2: $i] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) =
% 28.03/4.54        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 28.03/4.54      (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 28.03/4.54  
% 28.03/4.54  Further assumptions not needed in the proof:
% 28.03/4.54  --------------------------------------------
% 28.03/4.54  antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 28.03/4.54  commutativity_k2_xboole_0, commutativity_k3_xboole_0, d1_tarski, d1_xboole_0,
% 28.03/4.54  d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_xboole_0, d5_tarski, d7_xboole_0,
% 28.03/4.54  d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski,
% 28.03/4.54  dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0,
% 28.03/4.54  dt_k4_tarski, dt_k4_xboole_0, dt_m1_subset_1, existence_m1_subset_1,
% 28.03/4.54  fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 28.03/4.54  idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1,
% 28.03/4.54  l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1,
% 28.03/4.54  l50_zfmisc_1, l55_zfmisc_1, rc2_xboole_0, reflexivity_r1_tarski, t106_zfmisc_1,
% 28.03/4.54  t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1,
% 28.03/4.54  t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t26_xboole_1, t28_xboole_1,
% 28.03/4.54  t2_boole, t2_tarski, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_zfmisc_1,
% 28.03/4.54  t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_xboole_0, t40_xboole_1,
% 28.03/4.54  t45_xboole_1, t46_zfmisc_1, t4_boole, t60_xboole_1, t63_xboole_1, t65_zfmisc_1,
% 28.03/4.54  t69_enumset1, t6_zfmisc_1, t7_boole, t7_xboole_1, t8_xboole_1, t8_zfmisc_1,
% 28.03/4.54  t92_zfmisc_1, t9_tarski, t9_zfmisc_1
% 28.03/4.54  
% 28.03/4.54  Those formulas are unsatisfiable:
% 28.03/4.54  ---------------------------------
% 28.03/4.54  
% 28.03/4.54  Begin of proof
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d10_xboole_0) implies:
% 28.03/4.54  |   (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ~
% 28.03/4.54  |          $i(v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) =
% 28.03/4.54  |            v2))
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d1_zfmisc_1) implies:
% 28.03/4.54  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v1) |  ~
% 28.03/4.54  |          $i(v0) | ( ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (subset(v2, v0) =
% 28.03/4.54  |                v3) |  ~ $i(v2) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) =
% 28.03/4.54  |                v4)) &  ! [v2: $i] : ( ~ (subset(v2, v0) = 0) |  ~ $i(v2) |
% 28.03/4.54  |              in(v2, v1) = 0)))
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d2_subset_1) implies:
% 28.03/4.54  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 28.03/4.54  |           ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (empty(v0) = v3
% 28.03/4.54  |            & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 =
% 28.03/4.54  |                    0) | v4 = 0)))))
% 28.03/4.54  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 28.03/4.54  |           ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (empty(v1) = v4
% 28.03/4.54  |            & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2
% 28.03/4.54  |                    = 0) | v4 = 0)))))
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d3_tarski) implies:
% 28.03/4.54  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 28.03/4.54  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 28.03/4.54  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d4_tarski) implies:
% 28.03/4.54  |   (6)   ! [v0: $i] :  ! [v1: $i] : ( ~ (union(v0) = v1) |  ~ $i(v1) |  ~
% 28.03/4.54  |          $i(v0) | ( ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (in(v2, v1) = v3)
% 28.03/4.54  |              |  ~ $i(v2) |  ! [v4: $i] : ( ~ (in(v2, v4) = 0) |  ~ $i(v4) |  ?
% 28.03/4.54  |                [v5: int] : ( ~ (v5 = 0) & in(v4, v0) = v5))) &  ! [v2: $i] : (
% 28.03/4.54  |              ~ (in(v2, v1) = 0) |  ~ $i(v2) |  ? [v3: $i] : (in(v3, v0) = 0 &
% 28.03/4.54  |                in(v2, v3) = 0 & $i(v3)))))
% 28.03/4.54  | 
% 28.03/4.54  | ALPHA: (d4_xboole_0) implies:
% 28.03/4.55  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_difference(v0, v1) =
% 28.03/4.55  |            v2) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4:
% 28.03/4.55  |              any] : ( ~ (in(v3, v0) = v4) |  ~ $i(v3) |  ? [v5: any] :  ? [v6:
% 28.03/4.55  |                any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4
% 28.03/4.55  |                    = 0 &  ~ (v6 = 0))))) &  ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 28.03/4.55  |              |  ~ $i(v3) |  ? [v4: any] :  ? [v5: any] : (in(v3, v2) = v5 &
% 28.03/4.55  |                in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t1_zfmisc_1) implies:
% 28.03/4.55  |   (8)   ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 28.03/4.55  |          $i(v0))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t2_xboole_1) implies:
% 28.03/4.55  |   (9)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1)
% 28.03/4.55  |          |  ~ $i(v0))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t37_xboole_1) implies:
% 28.03/4.55  |   (10)   ! [v0: $i] :  ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) |
% 28.03/4.55  |            ~ $i(v1) |  ~ $i(v0) | subset(v0, v1) = 0)
% 28.03/4.55  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = empty_set |  ~
% 28.03/4.55  |           (set_difference(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 28.03/4.55  |           : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t3_boole) implies:
% 28.03/4.55  |   (12)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (set_difference(v0,
% 28.03/4.55  |               empty_set) = v1) |  ~ $i(v0))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t3_xboole_1) implies:
% 28.03/4.55  |   (13)   ! [v0: $i] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0) |  ~
% 28.03/4.55  |           $i(v0))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t4_xboole_0) implies:
% 28.03/4.55  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0,
% 28.03/4.55  |               v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0)
% 28.03/4.55  |             & disjoint(v0, v1) = v3) |  ! [v3: $i] : ( ~ (in(v3, v2) = 0) |  ~
% 28.03/4.55  |             $i(v3)))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t6_boole) implies:
% 28.03/4.55  |   (15)   ! [v0: $i] : (v0 = empty_set |  ~ (empty(v0) = 0) |  ~ $i(v0))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t83_xboole_1) implies:
% 28.03/4.55  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (disjoint(v0,
% 28.03/4.55  |               v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] : ( ~ (v3 = v0)
% 28.03/4.55  |             & set_difference(v0, v1) = v3 & $i(v3)))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (t50_subset_1) implies:
% 28.03/4.55  |   (17)  $i(empty_set)
% 28.03/4.55  |   (18)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v0 = empty_set) & powerset(v0) = v1 &
% 28.03/4.55  |           $i(v1) & $i(v0) &  ? [v2: $i] :  ? [v3: $i] : (subset_complement(v0,
% 28.03/4.55  |               v2) = v3 & element(v2, v1) = 0 & $i(v3) & $i(v2) &  ? [v4: $i] :
% 28.03/4.55  |              ? [v5: int] :  ? [v6: int] : ( ~ (v6 = 0) &  ~ (v5 = 0) &
% 28.03/4.55  |               element(v4, v0) = 0 & in(v4, v3) = v6 & in(v4, v2) = v5 &
% 28.03/4.55  |               $i(v4))))
% 28.03/4.55  | 
% 28.03/4.55  | ALPHA: (function-axioms) implies:
% 28.03/4.55  |   (19)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 28.03/4.55  |         : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 28.03/4.55  |   (20)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 28.03/4.55  |         :  ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) =
% 28.03/4.55  |             v0))
% 28.03/4.55  |   (21)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 28.03/4.55  |         :  ! [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3,
% 28.03/4.55  |               v2) = v0))
% 28.03/4.55  |   (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 28.03/4.55  |           (subset_complement(v3, v2) = v1) |  ~ (subset_complement(v3, v2) =
% 28.03/4.55  |             v0))
% 28.03/4.55  |   (23)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 28.03/4.55  |         :  ! [v3: $i] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~
% 28.03/4.55  |           (disjoint(v3, v2) = v0))
% 28.03/4.55  | 
% 28.03/4.56  | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_91_0 gives:
% 28.03/4.56  |   (24)  empty(all_91_0) = 0 & $i(all_91_0)
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (24) implies:
% 28.03/4.56  |   (25)  $i(all_91_0)
% 28.03/4.56  |   (26)  empty(all_91_0) = 0
% 28.03/4.56  | 
% 28.03/4.56  | DELTA: instantiating (8) with fresh symbol all_95_0 gives:
% 28.03/4.56  |   (27)  powerset(empty_set) = all_95_0 & singleton(empty_set) = all_95_0 &
% 28.03/4.56  |         $i(all_95_0)
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (27) implies:
% 28.03/4.56  |   (28)  $i(all_95_0)
% 28.03/4.56  |   (29)  powerset(empty_set) = all_95_0
% 28.03/4.56  | 
% 28.03/4.56  | DELTA: instantiating (18) with fresh symbols all_114_0, all_114_1 gives:
% 28.03/4.56  |   (30)   ~ (all_114_1 = empty_set) & powerset(all_114_1) = all_114_0 &
% 28.03/4.56  |         $i(all_114_0) & $i(all_114_1) &  ? [v0: $i] :  ? [v1: $i] :
% 28.03/4.56  |         (subset_complement(all_114_1, v0) = v1 & element(v0, all_114_0) = 0 &
% 28.03/4.56  |           $i(v1) & $i(v0) &  ? [v2: $i] :  ? [v3: int] :  ? [v4: int] : ( ~
% 28.03/4.56  |             (v4 = 0) &  ~ (v3 = 0) & element(v2, all_114_1) = 0 & in(v2, v1) =
% 28.03/4.56  |             v4 & in(v2, v0) = v3 & $i(v2)))
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (30) implies:
% 28.03/4.56  |   (31)   ~ (all_114_1 = empty_set)
% 28.03/4.56  |   (32)  $i(all_114_1)
% 28.03/4.56  |   (33)  $i(all_114_0)
% 28.03/4.56  |   (34)  powerset(all_114_1) = all_114_0
% 28.03/4.56  |   (35)   ? [v0: $i] :  ? [v1: $i] : (subset_complement(all_114_1, v0) = v1 &
% 28.03/4.56  |           element(v0, all_114_0) = 0 & $i(v1) & $i(v0) &  ? [v2: $i] :  ? [v3:
% 28.03/4.56  |             int] :  ? [v4: int] : ( ~ (v4 = 0) &  ~ (v3 = 0) & element(v2,
% 28.03/4.56  |               all_114_1) = 0 & in(v2, v1) = v4 & in(v2, v0) = v3 & $i(v2)))
% 28.03/4.56  | 
% 28.03/4.56  | DELTA: instantiating (35) with fresh symbols all_128_0, all_128_1 gives:
% 28.03/4.56  |   (36)  subset_complement(all_114_1, all_128_1) = all_128_0 &
% 28.03/4.56  |         element(all_128_1, all_114_0) = 0 & $i(all_128_0) & $i(all_128_1) &  ?
% 28.03/4.56  |         [v0: $i] :  ? [v1: int] :  ? [v2: int] : ( ~ (v2 = 0) &  ~ (v1 = 0) &
% 28.03/4.56  |           element(v0, all_114_1) = 0 & in(v0, all_128_0) = v2 & in(v0,
% 28.03/4.56  |             all_128_1) = v1 & $i(v0))
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (36) implies:
% 28.03/4.56  |   (37)  $i(all_128_1)
% 28.03/4.56  |   (38)  element(all_128_1, all_114_0) = 0
% 28.03/4.56  |   (39)  subset_complement(all_114_1, all_128_1) = all_128_0
% 28.03/4.56  |   (40)   ? [v0: $i] :  ? [v1: int] :  ? [v2: int] : ( ~ (v2 = 0) &  ~ (v1 = 0)
% 28.03/4.56  |           & element(v0, all_114_1) = 0 & in(v0, all_128_0) = v2 & in(v0,
% 28.03/4.56  |             all_128_1) = v1 & $i(v0))
% 28.03/4.56  | 
% 28.03/4.56  | DELTA: instantiating (40) with fresh symbols all_130_0, all_130_1, all_130_2
% 28.03/4.56  |        gives:
% 28.03/4.56  |   (41)   ~ (all_130_0 = 0) &  ~ (all_130_1 = 0) & element(all_130_2,
% 28.03/4.56  |           all_114_1) = 0 & in(all_130_2, all_128_0) = all_130_0 &
% 28.03/4.56  |         in(all_130_2, all_128_1) = all_130_1 & $i(all_130_2)
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (41) implies:
% 28.03/4.56  |   (42)   ~ (all_130_1 = 0)
% 28.03/4.56  |   (43)   ~ (all_130_0 = 0)
% 28.03/4.56  |   (44)  $i(all_130_2)
% 28.03/4.56  |   (45)  in(all_130_2, all_128_1) = all_130_1
% 28.03/4.56  |   (46)  in(all_130_2, all_128_0) = all_130_0
% 28.03/4.56  |   (47)  element(all_130_2, all_114_1) = 0
% 28.03/4.56  | 
% 28.03/4.56  | GROUND_INST: instantiating (2) with empty_set, all_95_0, simplifying with
% 28.03/4.56  |              (17), (28), (29) gives:
% 28.03/4.56  |   (48)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, empty_set) = v1)
% 28.03/4.56  |           |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_95_0) = v2))
% 28.03/4.56  |         &  ! [v0: $i] : ( ~ (subset(v0, empty_set) = 0) |  ~ $i(v0) | in(v0,
% 28.03/4.56  |             all_95_0) = 0)
% 28.03/4.56  | 
% 28.03/4.56  | ALPHA: (48) implies:
% 28.03/4.56  |   (49)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, empty_set) = v1)
% 28.03/4.56  |           |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_95_0) = v2))
% 28.03/4.56  | 
% 28.03/4.56  | GROUND_INST: instantiating (t99_zfmisc_1) with empty_set, all_95_0,
% 28.03/4.56  |              simplifying with (17), (29) gives:
% 28.03/4.56  |   (50)  union(all_95_0) = empty_set
% 28.03/4.56  | 
% 28.03/4.56  | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_95_0,
% 28.03/4.56  |              simplifying with (17), (29) gives:
% 28.03/4.56  |   (51)   ? [v0: $i] : (element(v0, all_95_0) = 0 & empty(v0) = 0 & $i(v0))
% 28.03/4.56  | 
% 28.03/4.57  | GROUND_INST: instantiating (2) with all_114_1, all_114_0, simplifying with
% 28.03/4.57  |              (32), (33), (34) gives:
% 28.03/4.57  |   (52)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, all_114_1) = v1)
% 28.03/4.57  |           |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_114_0) = v2))
% 28.03/4.57  |         &  ! [v0: $i] : ( ~ (subset(v0, all_114_1) = 0) |  ~ $i(v0) | in(v0,
% 28.03/4.57  |             all_114_0) = 0)
% 28.03/4.57  | 
% 28.03/4.57  | ALPHA: (52) implies:
% 28.03/4.57  |   (53)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, all_114_1) = v1)
% 28.03/4.57  |           |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_114_0) = v2))
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (rc1_subset_1) with all_114_1, all_114_0,
% 28.03/4.57  |              simplifying with (32), (34) gives:
% 28.03/4.57  |   (54)  empty(all_114_1) = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 28.03/4.57  |           element(v0, all_114_0) = 0 & empty(v0) = v1 & $i(v0))
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (fc1_subset_1) with all_114_1, all_114_0,
% 28.03/4.57  |              simplifying with (32), (34) gives:
% 28.03/4.57  |   (55)   ? [v0: int] : ( ~ (v0 = 0) & empty(all_114_0) = v0)
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (rc2_subset_1) with all_114_1, all_114_0,
% 28.03/4.57  |              simplifying with (32), (34) gives:
% 28.03/4.57  |   (56)   ? [v0: $i] : (element(v0, all_114_0) = 0 & empty(v0) = 0 & $i(v0))
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (15) with all_91_0, simplifying with (25), (26)
% 28.03/4.57  |              gives:
% 28.03/4.57  |   (57)  all_91_0 = empty_set
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (d5_subset_1) with all_114_1, all_128_1, all_114_0,
% 28.03/4.57  |              simplifying with (32), (34), (37), (38) gives:
% 28.03/4.57  |   (58)   ? [v0: $i] : (subset_complement(all_114_1, all_128_1) = v0 &
% 28.03/4.57  |           set_difference(all_114_1, all_128_1) = v0 & $i(v0))
% 28.03/4.57  | 
% 28.03/4.57  | GROUND_INST: instantiating (t43_subset_1) with all_114_1, all_128_1,
% 28.03/4.57  |              all_114_0, simplifying with (32), (34), (37), (38) gives:
% 28.41/4.57  |   (59)   ! [v0: $i] : ( ~ (element(v0, all_114_0) = 0) |  ~ $i(v0) |  ? [v1:
% 28.41/4.57  |             any] :  ? [v2: $i] :  ? [v3: any] : (disjoint(all_128_1, v0) = v1
% 28.41/4.57  |             & subset_complement(all_114_1, v0) = v2 & subset(all_128_1, v2) =
% 28.41/4.57  |             v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 28.41/4.57  | 
% 28.41/4.57  | GROUND_INST: instantiating (3) with all_114_0, all_128_1, 0, simplifying with
% 28.41/4.57  |              (33), (37), (38) gives:
% 28.41/4.57  |   (60)   ? [v0: any] :  ? [v1: any] : (empty(all_114_0) = v0 & in(all_128_1,
% 28.41/4.57  |             all_114_0) = v1 & (v1 = 0 | v0 = 0))
% 28.41/4.57  | 
% 28.41/4.57  | GROUND_INST: instantiating (4) with all_114_1, all_130_2, 0, simplifying with
% 28.41/4.57  |              (32), (44), (47) gives:
% 28.41/4.57  |   (61)   ? [v0: any] :  ? [v1: any] : (empty(all_130_2) = v1 &
% 28.41/4.57  |           empty(all_114_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 28.41/4.57  | 
% 28.41/4.57  | GROUND_INST: instantiating (3) with all_114_1, all_130_2, 0, simplifying with
% 28.41/4.57  |              (32), (44), (47) gives:
% 28.41/4.57  |   (62)   ? [v0: any] :  ? [v1: any] : (empty(all_114_1) = v0 & in(all_130_2,
% 28.41/4.57  |             all_114_1) = v1 & (v1 = 0 | v0 = 0))
% 28.41/4.57  | 
% 28.41/4.57  | GROUND_INST: instantiating (59) with all_128_1, simplifying with (37), (38)
% 28.41/4.57  |              gives:
% 28.41/4.57  |   (63)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_128_1,
% 28.41/4.57  |             all_128_1) = v0 & subset_complement(all_114_1, all_128_1) = v1 &
% 28.41/4.57  |           subset(all_128_1, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~
% 28.41/4.57  |             (v0 = 0) | v2 = 0))
% 28.41/4.57  | 
% 28.41/4.57  | DELTA: instantiating (55) with fresh symbol all_145_0 gives:
% 28.41/4.57  |   (64)   ~ (all_145_0 = 0) & empty(all_114_0) = all_145_0
% 28.42/4.57  | 
% 28.42/4.57  | ALPHA: (64) implies:
% 28.42/4.57  |   (65)   ~ (all_145_0 = 0)
% 28.42/4.57  |   (66)  empty(all_114_0) = all_145_0
% 28.42/4.57  | 
% 28.42/4.57  | DELTA: instantiating (51) with fresh symbol all_147_0 gives:
% 28.42/4.57  |   (67)  element(all_147_0, all_95_0) = 0 & empty(all_147_0) = 0 &
% 28.42/4.57  |         $i(all_147_0)
% 28.42/4.57  | 
% 28.42/4.57  | ALPHA: (67) implies:
% 28.42/4.57  |   (68)  $i(all_147_0)
% 28.42/4.57  |   (69)  empty(all_147_0) = 0
% 28.42/4.57  |   (70)  element(all_147_0, all_95_0) = 0
% 28.42/4.57  | 
% 28.42/4.57  | DELTA: instantiating (58) with fresh symbol all_149_0 gives:
% 28.42/4.57  |   (71)  subset_complement(all_114_1, all_128_1) = all_149_0 &
% 28.42/4.57  |         set_difference(all_114_1, all_128_1) = all_149_0 & $i(all_149_0)
% 28.42/4.57  | 
% 28.42/4.57  | ALPHA: (71) implies:
% 28.42/4.57  |   (72)  $i(all_149_0)
% 28.42/4.57  |   (73)  set_difference(all_114_1, all_128_1) = all_149_0
% 28.42/4.57  |   (74)  subset_complement(all_114_1, all_128_1) = all_149_0
% 28.42/4.57  | 
% 28.42/4.57  | DELTA: instantiating (56) with fresh symbol all_151_0 gives:
% 28.42/4.57  |   (75)  element(all_151_0, all_114_0) = 0 & empty(all_151_0) = 0 &
% 28.42/4.57  |         $i(all_151_0)
% 28.42/4.57  | 
% 28.42/4.57  | ALPHA: (75) implies:
% 28.42/4.57  |   (76)  $i(all_151_0)
% 28.42/4.57  |   (77)  empty(all_151_0) = 0
% 28.42/4.57  |   (78)  element(all_151_0, all_114_0) = 0
% 28.42/4.57  | 
% 28.42/4.57  | DELTA: instantiating (61) with fresh symbols all_153_0, all_153_1 gives:
% 28.42/4.57  |   (79)  empty(all_130_2) = all_153_0 & empty(all_114_1) = all_153_1 & ( ~
% 28.42/4.57  |           (all_153_1 = 0) | all_153_0 = 0)
% 28.42/4.57  | 
% 28.42/4.57  | ALPHA: (79) implies:
% 28.42/4.57  |   (80)  empty(all_114_1) = all_153_1
% 28.42/4.57  |   (81)  empty(all_130_2) = all_153_0
% 28.42/4.57  |   (82)   ~ (all_153_1 = 0) | all_153_0 = 0
% 28.42/4.57  | 
% 28.42/4.57  | DELTA: instantiating (62) with fresh symbols all_155_0, all_155_1 gives:
% 28.42/4.58  |   (83)  empty(all_114_1) = all_155_1 & in(all_130_2, all_114_1) = all_155_0 &
% 28.42/4.58  |         (all_155_0 = 0 | all_155_1 = 0)
% 28.42/4.58  | 
% 28.42/4.58  | ALPHA: (83) implies:
% 28.42/4.58  |   (84)  in(all_130_2, all_114_1) = all_155_0
% 28.42/4.58  |   (85)  empty(all_114_1) = all_155_1
% 28.42/4.58  |   (86)  all_155_0 = 0 | all_155_1 = 0
% 28.42/4.58  | 
% 28.42/4.58  | DELTA: instantiating (60) with fresh symbols all_159_0, all_159_1 gives:
% 28.42/4.58  |   (87)  empty(all_114_0) = all_159_1 & in(all_128_1, all_114_0) = all_159_0 &
% 28.42/4.58  |         (all_159_0 = 0 | all_159_1 = 0)
% 28.42/4.58  | 
% 28.42/4.58  | ALPHA: (87) implies:
% 28.42/4.58  |   (88)  empty(all_114_0) = all_159_1
% 28.42/4.58  |   (89)  all_159_0 = 0 | all_159_1 = 0
% 28.42/4.58  | 
% 28.42/4.58  | DELTA: instantiating (63) with fresh symbols all_161_0, all_161_1, all_161_2
% 28.42/4.58  |        gives:
% 28.42/4.58  |   (90)  disjoint(all_128_1, all_128_1) = all_161_2 &
% 28.42/4.58  |         subset_complement(all_114_1, all_128_1) = all_161_1 &
% 28.42/4.58  |         subset(all_128_1, all_161_1) = all_161_0 & $i(all_161_1) & ( ~
% 28.42/4.58  |           (all_161_0 = 0) | all_161_2 = 0) & ( ~ (all_161_2 = 0) | all_161_0 =
% 28.42/4.58  |           0)
% 28.42/4.58  | 
% 28.42/4.58  | ALPHA: (90) implies:
% 28.42/4.58  |   (91)  subset(all_128_1, all_161_1) = all_161_0
% 28.42/4.58  |   (92)  subset_complement(all_114_1, all_128_1) = all_161_1
% 28.42/4.58  |   (93)  disjoint(all_128_1, all_128_1) = all_161_2
% 28.42/4.58  |   (94)   ~ (all_161_2 = 0) | all_161_0 = 0
% 28.42/4.58  | 
% 28.42/4.58  | GROUND_INST: instantiating (19) with all_153_1, all_155_1, all_114_1,
% 28.42/4.58  |              simplifying with (80), (85) gives:
% 28.42/4.58  |   (95)  all_155_1 = all_153_1
% 28.42/4.58  | 
% 28.42/4.58  | GROUND_INST: instantiating (19) with all_145_0, all_159_1, all_114_0,
% 28.42/4.58  |              simplifying with (66), (88) gives:
% 28.42/4.58  |   (96)  all_159_1 = all_145_0
% 28.42/4.58  | 
% 28.42/4.58  | GROUND_INST: instantiating (22) with all_128_0, all_161_1, all_128_1,
% 28.42/4.58  |              all_114_1, simplifying with (39), (92) gives:
% 28.42/4.58  |   (97)  all_161_1 = all_128_0
% 28.42/4.58  | 
% 28.42/4.58  | GROUND_INST: instantiating (22) with all_149_0, all_161_1, all_128_1,
% 28.42/4.58  |              all_114_1, simplifying with (74), (92) gives:
% 28.42/4.58  |   (98)  all_161_1 = all_149_0
% 28.42/4.58  | 
% 28.42/4.58  | COMBINE_EQS: (97), (98) imply:
% 28.42/4.58  |   (99)  all_149_0 = all_128_0
% 28.42/4.58  | 
% 28.42/4.58  | REDUCE: (73), (99) imply:
% 28.42/4.58  |   (100)  set_difference(all_114_1, all_128_1) = all_128_0
% 28.42/4.58  | 
% 28.42/4.58  | REDUCE: (91), (97) imply:
% 28.42/4.58  |   (101)  subset(all_128_1, all_128_0) = all_161_0
% 28.42/4.58  | 
% 28.42/4.58  | REDUCE: (72), (99) imply:
% 28.42/4.58  |   (102)  $i(all_128_0)
% 28.42/4.58  | 
% 28.42/4.58  | BETA: splitting (89) gives:
% 28.42/4.58  | 
% 28.42/4.58  | Case 1:
% 28.42/4.58  | | 
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (t8_boole) with all_147_0, all_151_0, simplifying
% 28.42/4.58  | |              with (68), (69), (76), (77) gives:
% 28.42/4.58  | |   (103)  all_151_0 = all_147_0
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (15) with all_151_0, simplifying with (76), (77)
% 28.42/4.58  | |              gives:
% 28.42/4.58  | |   (104)  all_151_0 = empty_set
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (d5_subset_1) with empty_set, all_147_0,
% 28.42/4.58  | |              all_95_0, simplifying with (17), (29), (68), (70) gives:
% 28.42/4.58  | |   (105)   ? [v0: $i] : (subset_complement(empty_set, all_147_0) = v0 &
% 28.42/4.58  | |            set_difference(empty_set, all_147_0) = v0 & $i(v0))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (t43_subset_1) with empty_set, all_147_0,
% 28.42/4.58  | |              all_95_0, simplifying with (17), (29), (68), (70) gives:
% 28.42/4.58  | |   (106)   ! [v0: $i] : ( ~ (element(v0, all_95_0) = 0) |  ~ $i(v0) |  ? [v1:
% 28.42/4.58  | |              any] :  ? [v2: $i] :  ? [v3: any] : (disjoint(all_147_0, v0) =
% 28.42/4.58  | |              v1 & subset_complement(empty_set, v0) = v2 & subset(all_147_0,
% 28.42/4.58  | |                v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) |
% 28.42/4.58  | |                v3 = 0)))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (d5_subset_1) with all_114_1, all_151_0,
% 28.42/4.58  | |              all_114_0, simplifying with (32), (34), (76), (78) gives:
% 28.42/4.58  | |   (107)   ? [v0: $i] : (subset_complement(all_114_1, all_151_0) = v0 &
% 28.42/4.58  | |            set_difference(all_114_1, all_151_0) = v0 & $i(v0))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (t43_subset_1) with all_114_1, all_151_0,
% 28.42/4.58  | |              all_114_0, simplifying with (32), (34), (76), (78) gives:
% 28.42/4.58  | |   (108)   ! [v0: $i] : ( ~ (element(v0, all_114_0) = 0) |  ~ $i(v0) |  ?
% 28.42/4.58  | |            [v1: any] :  ? [v2: $i] :  ? [v3: any] : (disjoint(all_151_0, v0)
% 28.42/4.58  | |              = v1 & subset_complement(all_114_1, v0) = v2 &
% 28.42/4.58  | |              subset(all_151_0, v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) &
% 28.42/4.58  | |              ( ~ (v1 = 0) | v3 = 0)))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (59) with all_151_0, simplifying with (76), (78)
% 28.42/4.58  | |              gives:
% 28.42/4.58  | |   (109)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_128_1,
% 28.42/4.58  | |              all_151_0) = v0 & subset_complement(all_114_1, all_151_0) = v1
% 28.42/4.58  | |            & subset(all_128_1, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.58  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (6) with all_95_0, empty_set, simplifying with
% 28.42/4.58  | |              (17), (28), (50) gives:
% 28.42/4.58  | |   (110)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (in(v0, empty_set) = v1)
% 28.42/4.58  | |            |  ~ $i(v0) |  ! [v2: $i] : ( ~ (in(v0, v2) = 0) |  ~ $i(v2) |  ?
% 28.42/4.58  | |              [v3: int] : ( ~ (v3 = 0) & in(v2, all_95_0) = v3))) &  ! [v0:
% 28.42/4.58  | |            $i] : ( ~ (in(v0, empty_set) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 28.42/4.58  | |            (in(v1, all_95_0) = 0 & in(v0, v1) = 0 & $i(v1)))
% 28.42/4.58  | | 
% 28.42/4.58  | | ALPHA: (110) implies:
% 28.42/4.58  | |   (111)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (in(v0, empty_set) = v1)
% 28.42/4.58  | |            |  ~ $i(v0) |  ! [v2: $i] : ( ~ (in(v0, v2) = 0) |  ~ $i(v2) |  ?
% 28.42/4.58  | |              [v3: int] : ( ~ (v3 = 0) & in(v2, all_95_0) = v3)))
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (11) with all_114_1, all_128_1, all_128_0,
% 28.42/4.58  | |              simplifying with (32), (37), (100) gives:
% 28.42/4.58  | |   (112)  all_128_0 = empty_set |  ? [v0: int] : ( ~ (v0 = 0) &
% 28.42/4.58  | |            subset(all_114_1, all_128_1) = v0)
% 28.42/4.58  | | 
% 28.42/4.58  | | GROUND_INST: instantiating (7) with all_114_1, all_128_1, all_128_0,
% 28.42/4.59  | |              simplifying with (32), (37), (100), (102) gives:
% 28.42/4.59  | |   (113)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0, all_114_1) = v1) |  ~
% 28.42/4.59  | |            $i(v0) |  ? [v2: any] :  ? [v3: any] : (in(v0, all_128_0) = v2 &
% 28.42/4.59  | |              in(v0, all_128_1) = v3 & ( ~ (v2 = 0) | (v1 = 0 &  ~ (v3 =
% 28.42/4.59  | |                    0))))) &  ! [v0: $i] : ( ~ (in(v0, all_114_1) = 0) |  ~
% 28.42/4.59  | |            $i(v0) |  ? [v1: any] :  ? [v2: any] : (in(v0, all_128_0) = v2 &
% 28.42/4.59  | |              in(v0, all_128_1) = v1 & (v2 = 0 | v1 = 0)))
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (113) implies:
% 28.42/4.59  | |   (114)   ! [v0: $i] : ( ~ (in(v0, all_114_1) = 0) |  ~ $i(v0) |  ? [v1:
% 28.42/4.59  | |              any] :  ? [v2: any] : (in(v0, all_128_0) = v2 & in(v0,
% 28.42/4.59  | |                all_128_1) = v1 & (v2 = 0 | v1 = 0)))
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (16) with all_128_1, all_128_1, all_161_2,
% 28.42/4.59  | |              simplifying with (37), (93) gives:
% 28.42/4.59  | |   (115)  all_161_2 = 0 |  ? [v0: any] : ( ~ (v0 = all_128_1) &
% 28.42/4.59  | |            set_difference(all_128_1, all_128_1) = v0 & $i(v0))
% 28.42/4.59  | | 
% 28.42/4.59  | | COMBINE_EQS: (103), (104) imply:
% 28.42/4.59  | |   (116)  all_147_0 = empty_set
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (108) with all_128_1, simplifying with (37), (38)
% 28.42/4.59  | |              gives:
% 28.42/4.59  | |   (117)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_151_0,
% 28.42/4.59  | |              all_128_1) = v0 & subset_complement(all_114_1, all_128_1) = v1
% 28.42/4.59  | |            & subset(all_151_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.59  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (108) with all_151_0, simplifying with (76), (78)
% 28.42/4.59  | |              gives:
% 28.42/4.59  | |   (118)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_151_0,
% 28.42/4.59  | |              all_151_0) = v0 & subset_complement(all_114_1, all_151_0) = v1
% 28.42/4.59  | |            & subset(all_151_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.59  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (106) with all_147_0, simplifying with (68), (70)
% 28.42/4.59  | |              gives:
% 28.42/4.59  | |   (119)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_147_0,
% 28.42/4.59  | |              all_147_0) = v0 & subset_complement(empty_set, all_147_0) = v1
% 28.42/4.59  | |            & subset(all_147_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.59  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (107) with fresh symbol all_186_0 gives:
% 28.42/4.59  | |   (120)  subset_complement(all_114_1, all_151_0) = all_186_0 &
% 28.42/4.59  | |          set_difference(all_114_1, all_151_0) = all_186_0 & $i(all_186_0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (120) implies:
% 28.42/4.59  | |   (121)  set_difference(all_114_1, all_151_0) = all_186_0
% 28.42/4.59  | |   (122)  subset_complement(all_114_1, all_151_0) = all_186_0
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (105) with fresh symbol all_188_0 gives:
% 28.42/4.59  | |   (123)  subset_complement(empty_set, all_147_0) = all_188_0 &
% 28.42/4.59  | |          set_difference(empty_set, all_147_0) = all_188_0 & $i(all_188_0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (123) implies:
% 28.42/4.59  | |   (124)  set_difference(empty_set, all_147_0) = all_188_0
% 28.42/4.59  | |   (125)  subset_complement(empty_set, all_147_0) = all_188_0
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (109) with fresh symbols all_194_0, all_194_1,
% 28.42/4.59  | |        all_194_2 gives:
% 28.42/4.59  | |   (126)  disjoint(all_128_1, all_151_0) = all_194_2 &
% 28.42/4.59  | |          subset_complement(all_114_1, all_151_0) = all_194_1 &
% 28.42/4.59  | |          subset(all_128_1, all_194_1) = all_194_0 & $i(all_194_1) & ( ~
% 28.42/4.59  | |            (all_194_0 = 0) | all_194_2 = 0) & ( ~ (all_194_2 = 0) |
% 28.42/4.59  | |            all_194_0 = 0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (126) implies:
% 28.42/4.59  | |   (127)  $i(all_194_1)
% 28.42/4.59  | |   (128)  subset(all_128_1, all_194_1) = all_194_0
% 28.42/4.59  | |   (129)  subset_complement(all_114_1, all_151_0) = all_194_1
% 28.42/4.59  | |   (130)  disjoint(all_128_1, all_151_0) = all_194_2
% 28.42/4.59  | |   (131)   ~ (all_194_2 = 0) | all_194_0 = 0
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (118) with fresh symbols all_196_0, all_196_1,
% 28.42/4.59  | |        all_196_2 gives:
% 28.42/4.59  | |   (132)  disjoint(all_151_0, all_151_0) = all_196_2 &
% 28.42/4.59  | |          subset_complement(all_114_1, all_151_0) = all_196_1 &
% 28.42/4.59  | |          subset(all_151_0, all_196_1) = all_196_0 & $i(all_196_1) & ( ~
% 28.42/4.59  | |            (all_196_0 = 0) | all_196_2 = 0) & ( ~ (all_196_2 = 0) |
% 28.42/4.59  | |            all_196_0 = 0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (132) implies:
% 28.42/4.59  | |   (133)  subset_complement(all_114_1, all_151_0) = all_196_1
% 28.42/4.59  | |   (134)  disjoint(all_151_0, all_151_0) = all_196_2
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (117) with fresh symbols all_198_0, all_198_1,
% 28.42/4.59  | |        all_198_2 gives:
% 28.42/4.59  | |   (135)  disjoint(all_151_0, all_128_1) = all_198_2 &
% 28.42/4.59  | |          subset_complement(all_114_1, all_128_1) = all_198_1 &
% 28.42/4.59  | |          subset(all_151_0, all_198_1) = all_198_0 & $i(all_198_1) & ( ~
% 28.42/4.59  | |            (all_198_0 = 0) | all_198_2 = 0) & ( ~ (all_198_2 = 0) |
% 28.42/4.59  | |            all_198_0 = 0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (135) implies:
% 28.42/4.59  | |   (136)  $i(all_198_1)
% 28.42/4.59  | |   (137)  subset(all_151_0, all_198_1) = all_198_0
% 28.42/4.59  | |   (138)  subset_complement(all_114_1, all_128_1) = all_198_1
% 28.42/4.59  | |   (139)  disjoint(all_151_0, all_128_1) = all_198_2
% 28.42/4.59  | |   (140)   ~ (all_198_0 = 0) | all_198_2 = 0
% 28.42/4.59  | | 
% 28.42/4.59  | | DELTA: instantiating (119) with fresh symbols all_200_0, all_200_1,
% 28.42/4.59  | |        all_200_2 gives:
% 28.42/4.59  | |   (141)  disjoint(all_147_0, all_147_0) = all_200_2 &
% 28.42/4.59  | |          subset_complement(empty_set, all_147_0) = all_200_1 &
% 28.42/4.59  | |          subset(all_147_0, all_200_1) = all_200_0 & $i(all_200_1) & ( ~
% 28.42/4.59  | |            (all_200_0 = 0) | all_200_2 = 0) & ( ~ (all_200_2 = 0) |
% 28.42/4.59  | |            all_200_0 = 0)
% 28.42/4.59  | | 
% 28.42/4.59  | | ALPHA: (141) implies:
% 28.42/4.59  | |   (142)  $i(all_200_1)
% 28.42/4.59  | |   (143)  subset(all_147_0, all_200_1) = all_200_0
% 28.42/4.59  | |   (144)  subset_complement(empty_set, all_147_0) = all_200_1
% 28.42/4.59  | |   (145)  disjoint(all_147_0, all_147_0) = all_200_2
% 28.42/4.59  | |   (146)   ~ (all_200_0 = 0) | all_200_2 = 0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (134) imply:
% 28.42/4.59  | |   (147)  disjoint(empty_set, empty_set) = all_196_2
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (139) imply:
% 28.42/4.59  | |   (148)  disjoint(empty_set, all_128_1) = all_198_2
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (116), (145) imply:
% 28.42/4.59  | |   (149)  disjoint(empty_set, empty_set) = all_200_2
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (130) imply:
% 28.42/4.59  | |   (150)  disjoint(all_128_1, empty_set) = all_194_2
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (133) imply:
% 28.42/4.59  | |   (151)  subset_complement(all_114_1, empty_set) = all_196_1
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (129) imply:
% 28.42/4.59  | |   (152)  subset_complement(all_114_1, empty_set) = all_194_1
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (122) imply:
% 28.42/4.59  | |   (153)  subset_complement(all_114_1, empty_set) = all_186_0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (116), (144) imply:
% 28.42/4.59  | |   (154)  subset_complement(empty_set, empty_set) = all_200_1
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (116), (125) imply:
% 28.42/4.59  | |   (155)  subset_complement(empty_set, empty_set) = all_188_0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (121) imply:
% 28.42/4.59  | |   (156)  set_difference(all_114_1, empty_set) = all_186_0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (116), (124) imply:
% 28.42/4.59  | |   (157)  set_difference(empty_set, empty_set) = all_188_0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (78), (104) imply:
% 28.42/4.59  | |   (158)  element(empty_set, all_114_0) = 0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (70), (116) imply:
% 28.42/4.59  | |   (159)  element(empty_set, all_95_0) = 0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (104), (137) imply:
% 28.42/4.59  | |   (160)  subset(empty_set, all_198_1) = all_198_0
% 28.42/4.59  | | 
% 28.42/4.59  | | REDUCE: (116), (143) imply:
% 28.42/4.59  | |   (161)  subset(empty_set, all_200_1) = all_200_0
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (22) with all_188_0, all_200_1, empty_set,
% 28.42/4.59  | |              empty_set, simplifying with (154), (155) gives:
% 28.42/4.59  | |   (162)  all_200_1 = all_188_0
% 28.42/4.59  | | 
% 28.42/4.59  | | GROUND_INST: instantiating (22) with all_194_1, all_196_1, empty_set,
% 28.42/4.59  | |              all_114_1, simplifying with (151), (152) gives:
% 28.42/4.59  | |   (163)  all_196_1 = all_194_1
% 28.42/4.59  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (22) with all_186_0, all_196_1, empty_set,
% 28.42/4.60  | |              all_114_1, simplifying with (151), (153) gives:
% 28.42/4.60  | |   (164)  all_196_1 = all_186_0
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (22) with all_128_0, all_198_1, all_128_1,
% 28.42/4.60  | |              all_114_1, simplifying with (39), (138) gives:
% 28.42/4.60  | |   (165)  all_198_1 = all_128_0
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (23) with all_196_2, all_200_2, empty_set,
% 28.42/4.60  | |              empty_set, simplifying with (147), (149) gives:
% 28.42/4.60  | |   (166)  all_200_2 = all_196_2
% 28.42/4.60  | | 
% 28.42/4.60  | | COMBINE_EQS: (163), (164) imply:
% 28.42/4.60  | |   (167)  all_194_1 = all_186_0
% 28.42/4.60  | | 
% 28.42/4.60  | | SIMP: (167) implies:
% 28.42/4.60  | |   (168)  all_194_1 = all_186_0
% 28.42/4.60  | | 
% 28.42/4.60  | | REDUCE: (128), (168) imply:
% 28.42/4.60  | |   (169)  subset(all_128_1, all_186_0) = all_194_0
% 28.42/4.60  | | 
% 28.42/4.60  | | REDUCE: (161), (162) imply:
% 28.42/4.60  | |   (170)  subset(empty_set, all_188_0) = all_200_0
% 28.42/4.60  | | 
% 28.42/4.60  | | REDUCE: (160), (165) imply:
% 28.42/4.60  | |   (171)  subset(empty_set, all_128_0) = all_198_0
% 28.42/4.60  | | 
% 28.42/4.60  | | REDUCE: (142), (162) imply:
% 28.42/4.60  | |   (172)  $i(all_188_0)
% 28.42/4.60  | | 
% 28.42/4.60  | | REDUCE: (127), (168) imply:
% 28.42/4.60  | |   (173)  $i(all_186_0)
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (9) with all_128_0, all_198_0, simplifying with
% 28.42/4.60  | |              (102), (171) gives:
% 28.42/4.60  | |   (174)  all_198_0 = 0
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (9) with all_188_0, all_200_0, simplifying with
% 28.42/4.60  | |              (170), (172) gives:
% 28.42/4.60  | |   (175)  all_200_0 = 0
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (106) with empty_set, simplifying with (17),
% 28.42/4.60  | |              (159) gives:
% 28.42/4.60  | |   (176)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_147_0,
% 28.42/4.60  | |              empty_set) = v0 & subset_complement(empty_set, empty_set) = v1
% 28.42/4.60  | |            & subset(all_147_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.60  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (108) with empty_set, simplifying with (17),
% 28.42/4.60  | |              (158) gives:
% 28.42/4.60  | |   (177)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] : (disjoint(all_151_0,
% 28.42/4.60  | |              empty_set) = v0 & subset_complement(all_114_1, empty_set) = v1
% 28.42/4.60  | |            & subset(all_151_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) &
% 28.42/4.60  | |            ( ~ (v0 = 0) | v2 = 0))
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (12) with empty_set, all_188_0, simplifying with
% 28.42/4.60  | |              (17), (157) gives:
% 28.42/4.60  | |   (178)  all_188_0 = empty_set
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (12) with all_114_1, all_186_0, simplifying with
% 28.42/4.60  | |              (32), (156) gives:
% 28.42/4.60  | |   (179)  all_186_0 = all_114_1
% 28.42/4.60  | | 
% 28.42/4.60  | | GROUND_INST: instantiating (11) with all_114_1, empty_set, all_186_0,
% 28.42/4.60  | |              simplifying with (17), (32), (156) gives:
% 28.55/4.60  | |   (180)  all_186_0 = empty_set |  ? [v0: int] : ( ~ (v0 = 0) &
% 28.55/4.60  | |            subset(all_114_1, empty_set) = v0)
% 28.55/4.60  | | 
% 28.55/4.60  | | GROUND_INST: instantiating (7) with all_114_1, empty_set, all_186_0,
% 28.55/4.60  | |              simplifying with (17), (32), (156), (173) gives:
% 28.55/4.60  | |   (181)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0, all_114_1) = v1) |  ~
% 28.55/4.60  | |            $i(v0) |  ? [v2: any] :  ? [v3: any] : (in(v0, all_186_0) = v2 &
% 28.55/4.60  | |              in(v0, empty_set) = v3 & ( ~ (v2 = 0) | (v1 = 0 &  ~ (v3 =
% 28.55/4.60  | |                    0))))) &  ! [v0: $i] : ( ~ (in(v0, all_114_1) = 0) |  ~
% 28.55/4.60  | |            $i(v0) |  ? [v1: any] :  ? [v2: any] : (in(v0, all_186_0) = v2 &
% 28.55/4.60  | |              in(v0, empty_set) = v1 & (v2 = 0 | v1 = 0)))
% 28.55/4.60  | | 
% 28.55/4.60  | | ALPHA: (181) implies:
% 28.55/4.60  | |   (182)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0, all_114_1) = v1) |  ~
% 28.55/4.60  | |            $i(v0) |  ? [v2: any] :  ? [v3: any] : (in(v0, all_186_0) = v2 &
% 28.55/4.60  | |              in(v0, empty_set) = v3 & ( ~ (v2 = 0) | (v1 = 0 &  ~ (v3 =
% 28.55/4.60  | |                    0)))))
% 28.55/4.60  | | 
% 28.55/4.60  | | GROUND_INST: instantiating (182) with all_130_2, all_155_0, simplifying with
% 28.55/4.60  | |              (44), (84) gives:
% 28.55/4.60  | |   (183)   ? [v0: any] :  ? [v1: any] : (in(all_130_2, all_186_0) = v0 &
% 28.55/4.60  | |            in(all_130_2, empty_set) = v1 & ( ~ (v0 = 0) | (all_155_0 = 0 & 
% 28.55/4.60  | |                ~ (v1 = 0))))
% 28.55/4.60  | | 
% 28.55/4.60  | | DELTA: instantiating (183) with fresh symbols all_222_0, all_222_1 gives:
% 28.55/4.60  | |   (184)  in(all_130_2, all_186_0) = all_222_1 & in(all_130_2, empty_set) =
% 28.55/4.60  | |          all_222_0 & ( ~ (all_222_1 = 0) | (all_155_0 = 0 &  ~ (all_222_0 =
% 28.55/4.60  | |                0)))
% 28.55/4.60  | | 
% 28.55/4.60  | | ALPHA: (184) implies:
% 28.55/4.60  | |   (185)  in(all_130_2, all_186_0) = all_222_1
% 28.55/4.60  | | 
% 28.55/4.60  | | DELTA: instantiating (176) with fresh symbols all_224_0, all_224_1,
% 28.55/4.60  | |        all_224_2 gives:
% 28.55/4.60  | |   (186)  disjoint(all_147_0, empty_set) = all_224_2 &
% 28.55/4.60  | |          subset_complement(empty_set, empty_set) = all_224_1 &
% 28.55/4.60  | |          subset(all_147_0, all_224_1) = all_224_0 & $i(all_224_1) & ( ~
% 28.55/4.60  | |            (all_224_0 = 0) | all_224_2 = 0) & ( ~ (all_224_2 = 0) |
% 28.55/4.60  | |            all_224_0 = 0)
% 28.55/4.60  | | 
% 28.55/4.60  | | ALPHA: (186) implies:
% 28.55/4.60  | |   (187)  $i(all_224_1)
% 28.55/4.60  | |   (188)  subset_complement(empty_set, empty_set) = all_224_1
% 28.55/4.60  | |   (189)  disjoint(all_147_0, empty_set) = all_224_2
% 28.55/4.60  | | 
% 28.55/4.60  | | DELTA: instantiating (177) with fresh symbols all_226_0, all_226_1,
% 28.55/4.60  | |        all_226_2 gives:
% 28.55/4.60  | |   (190)  disjoint(all_151_0, empty_set) = all_226_2 &
% 28.55/4.60  | |          subset_complement(all_114_1, empty_set) = all_226_1 &
% 28.55/4.60  | |          subset(all_151_0, all_226_1) = all_226_0 & $i(all_226_1) & ( ~
% 28.55/4.60  | |            (all_226_0 = 0) | all_226_2 = 0) & ( ~ (all_226_2 = 0) |
% 28.55/4.60  | |            all_226_0 = 0)
% 28.55/4.60  | | 
% 28.55/4.60  | | ALPHA: (190) implies:
% 28.55/4.60  | |   (191)  $i(all_226_1)
% 28.55/4.60  | |   (192)  subset_complement(all_114_1, empty_set) = all_226_1
% 28.55/4.60  | |   (193)  disjoint(all_151_0, empty_set) = all_226_2
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (104), (193) imply:
% 28.55/4.60  | |   (194)  disjoint(empty_set, empty_set) = all_226_2
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (116), (189) imply:
% 28.55/4.60  | |   (195)  disjoint(empty_set, empty_set) = all_224_2
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (153), (179) imply:
% 28.55/4.60  | |   (196)  subset_complement(all_114_1, empty_set) = all_114_1
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (155), (178) imply:
% 28.55/4.60  | |   (197)  subset_complement(empty_set, empty_set) = empty_set
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (157), (178) imply:
% 28.55/4.60  | |   (198)  set_difference(empty_set, empty_set) = empty_set
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (169), (179) imply:
% 28.55/4.60  | |   (199)  subset(all_128_1, all_114_1) = all_194_0
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (171), (174) imply:
% 28.55/4.60  | |   (200)  subset(empty_set, all_128_0) = 0
% 28.55/4.60  | | 
% 28.55/4.60  | | REDUCE: (179), (185) imply:
% 28.55/4.60  | |   (201)  in(all_130_2, all_114_1) = all_222_1
% 28.55/4.60  | | 
% 28.55/4.60  | | BETA: splitting (146) gives:
% 28.55/4.60  | | 
% 28.55/4.60  | | Case 1:
% 28.55/4.60  | | | 
% 28.55/4.60  | | |   (202)   ~ (all_200_0 = 0)
% 28.55/4.60  | | | 
% 28.55/4.60  | | | REDUCE: (175), (202) imply:
% 28.55/4.60  | | |   (203)  $false
% 28.55/4.60  | | | 
% 28.55/4.60  | | | CLOSE: (203) is inconsistent.
% 28.55/4.60  | | | 
% 28.55/4.60  | | Case 2:
% 28.55/4.60  | | | 
% 28.55/4.61  | | |   (204)  all_200_2 = 0
% 28.55/4.61  | | | 
% 28.55/4.61  | | | COMBINE_EQS: (166), (204) imply:
% 28.55/4.61  | | |   (205)  all_196_2 = 0
% 28.55/4.61  | | | 
% 28.55/4.61  | | | SIMP: (205) implies:
% 28.55/4.61  | | |   (206)  all_196_2 = 0
% 28.55/4.61  | | | 
% 28.55/4.61  | | | REDUCE: (147), (206) imply:
% 28.55/4.61  | | |   (207)  disjoint(empty_set, empty_set) = 0
% 28.55/4.61  | | | 
% 28.55/4.61  | | | BETA: splitting (180) gives:
% 28.55/4.61  | | | 
% 28.55/4.61  | | | Case 1:
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | |   (208)  all_186_0 = empty_set
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | COMBINE_EQS: (179), (208) imply:
% 28.55/4.61  | | | |   (209)  all_114_1 = empty_set
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | SIMP: (209) implies:
% 28.55/4.61  | | | |   (210)  all_114_1 = empty_set
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | REDUCE: (31), (210) imply:
% 28.55/4.61  | | | |   (211)  $false
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | CLOSE: (211) is inconsistent.
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | Case 2:
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | |   (212)   ~ (all_186_0 = empty_set)
% 28.55/4.61  | | | |   (213)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_114_1, empty_set) =
% 28.55/4.61  | | | |            v0)
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | DELTA: instantiating (213) with fresh symbol all_235_0 gives:
% 28.55/4.61  | | | |   (214)   ~ (all_235_0 = 0) & subset(all_114_1, empty_set) = all_235_0
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | ALPHA: (214) implies:
% 28.55/4.61  | | | |   (215)   ~ (all_235_0 = 0)
% 28.55/4.61  | | | |   (216)  subset(all_114_1, empty_set) = all_235_0
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | BETA: splitting (140) gives:
% 28.55/4.61  | | | | 
% 28.55/4.61  | | | | Case 1:
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | |   (217)   ~ (all_198_0 = 0)
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | REDUCE: (174), (217) imply:
% 28.55/4.61  | | | | |   (218)  $false
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | CLOSE: (218) is inconsistent.
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | Case 2:
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | |   (219)  all_198_2 = 0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | REDUCE: (148), (219) imply:
% 28.55/4.61  | | | | |   (220)  disjoint(empty_set, all_128_1) = 0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (20) with all_155_0, all_222_1, all_114_1,
% 28.55/4.61  | | | | |              all_130_2, simplifying with (84), (201) gives:
% 28.55/4.61  | | | | |   (221)  all_222_1 = all_155_0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (22) with empty_set, all_224_1, empty_set,
% 28.55/4.61  | | | | |              empty_set, simplifying with (188), (197) gives:
% 28.55/4.61  | | | | |   (222)  all_224_1 = empty_set
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (22) with all_114_1, all_226_1, empty_set,
% 28.55/4.61  | | | | |              all_114_1, simplifying with (192), (196) gives:
% 28.55/4.61  | | | | |   (223)  all_226_1 = all_114_1
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (23) with all_224_2, all_226_2, empty_set,
% 28.55/4.61  | | | | |              empty_set, simplifying with (194), (195) gives:
% 28.55/4.61  | | | | |   (224)  all_226_2 = all_224_2
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (23) with 0, all_226_2, empty_set,
% 28.55/4.61  | | | | |              empty_set, simplifying with (194), (207) gives:
% 28.55/4.61  | | | | |   (225)  all_226_2 = 0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | COMBINE_EQS: (224), (225) imply:
% 28.55/4.61  | | | | |   (226)  all_224_2 = 0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (1) with empty_set, all_128_0, simplifying
% 28.55/4.61  | | | | |              with (17), (102), (200) gives:
% 28.55/4.61  | | | | |   (227)  all_128_0 = empty_set |  ? [v0: int] : ( ~ (v0 = 0) &
% 28.55/4.61  | | | | |            subset(all_128_0, empty_set) = v0)
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (5) with all_114_1, empty_set, all_235_0,
% 28.55/4.61  | | | | |              simplifying with (17), (32), (216) gives:
% 28.55/4.61  | | | | |   (228)  all_235_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 28.55/4.61  | | | | |            in(v0, all_114_1) = 0 & in(v0, empty_set) = v1 & $i(v0))
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (53) with all_128_1, all_194_0, simplifying
% 28.55/4.61  | | | | |              with (37), (199) gives:
% 28.55/4.61  | | | | |   (229)  all_194_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_128_1,
% 28.55/4.61  | | | | |              all_114_0) = v0)
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (t48_xboole_1) with empty_set, empty_set,
% 28.55/4.61  | | | | |              empty_set, empty_set, simplifying with (17), (198) gives:
% 28.55/4.61  | | | | |   (230)  set_intersection2(empty_set, empty_set) = empty_set
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | GROUND_INST: instantiating (symmetry_r1_xboole_0) with empty_set,
% 28.55/4.61  | | | | |              all_128_1, simplifying with (17), (37), (220) gives:
% 28.55/4.61  | | | | |   (231)  disjoint(all_128_1, empty_set) = 0
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | BETA: splitting (229) gives:
% 28.55/4.61  | | | | | 
% 28.55/4.61  | | | | | Case 1:
% 28.55/4.61  | | | | | | 
% 28.55/4.61  | | | | | |   (232)  all_194_0 = 0
% 28.55/4.61  | | | | | | 
% 28.55/4.61  | | | | | | REDUCE: (199), (232) imply:
% 28.55/4.61  | | | | | |   (233)  subset(all_128_1, all_114_1) = 0
% 28.55/4.61  | | | | | | 
% 28.55/4.61  | | | | | | BETA: splitting (228) gives:
% 28.55/4.61  | | | | | | 
% 28.55/4.61  | | | | | | Case 1:
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | |   (234)  all_235_0 = 0
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | REDUCE: (215), (234) imply:
% 28.55/4.61  | | | | | | |   (235)  $false
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | CLOSE: (235) is inconsistent.
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | Case 2:
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | |   (236)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 28.55/4.61  | | | | | | |              all_114_1) = 0 & in(v0, empty_set) = v1 & $i(v0))
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | DELTA: instantiating (236) with fresh symbols all_300_0, all_300_1
% 28.55/4.61  | | | | | | |        gives:
% 28.55/4.61  | | | | | | |   (237)   ~ (all_300_0 = 0) & in(all_300_1, all_114_1) = 0 &
% 28.55/4.61  | | | | | | |          in(all_300_1, empty_set) = all_300_0 & $i(all_300_1)
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | ALPHA: (237) implies:
% 28.55/4.61  | | | | | | |   (238)   ~ (all_300_0 = 0)
% 28.55/4.61  | | | | | | |   (239)  $i(all_300_1)
% 28.55/4.61  | | | | | | |   (240)  in(all_300_1, empty_set) = all_300_0
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | BETA: splitting (54) gives:
% 28.55/4.61  | | | | | | | 
% 28.55/4.61  | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | |   (241)  empty(all_114_1) = 0
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | GROUND_INST: instantiating (19) with all_153_1, 0, all_114_1,
% 28.55/4.61  | | | | | | | |              simplifying with (80), (241) gives:
% 28.55/4.61  | | | | | | | |   (242)  all_153_1 = 0
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | BETA: splitting (82) gives:
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | |   (243)   ~ (all_153_1 = 0)
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | REDUCE: (242), (243) imply:
% 28.55/4.61  | | | | | | | | |   (244)  $false
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | CLOSE: (244) is inconsistent.
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | Case 2:
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | |   (245)  all_153_0 = 0
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | REDUCE: (81), (245) imply:
% 28.55/4.61  | | | | | | | | |   (246)  empty(all_130_2) = 0
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_114_1,
% 28.55/4.61  | | | | | | | | |              all_130_2, simplifying with (32), (44), (241),
% 28.55/4.61  | | | | | | | | |              (246) gives:
% 28.55/4.61  | | | | | | | | |   (247)  all_130_2 = all_114_1
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | GROUND_INST: instantiating (15) with all_130_2, simplifying
% 28.55/4.61  | | | | | | | | |              with (44), (246) gives:
% 28.55/4.61  | | | | | | | | |   (248)  all_130_2 = empty_set
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | COMBINE_EQS: (247), (248) imply:
% 28.55/4.61  | | | | | | | | |   (249)  all_114_1 = empty_set
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | REDUCE: (31), (249) imply:
% 28.55/4.61  | | | | | | | | |   (250)  $false
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | CLOSE: (250) is inconsistent.
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | End of split
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | Case 2:
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | |   (251)   ~ (empty(all_114_1) = 0)
% 28.55/4.61  | | | | | | | |   (252)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 28.55/4.61  | | | | | | | |              all_114_0) = 0 & empty(v0) = v1 & $i(v0))
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | DELTA: instantiating (252) with fresh symbols all_359_0,
% 28.55/4.61  | | | | | | | |        all_359_1 gives:
% 28.55/4.61  | | | | | | | |   (253)   ~ (all_359_0 = 0) & element(all_359_1, all_114_0) = 0
% 28.55/4.61  | | | | | | | |          & empty(all_359_1) = all_359_0 & $i(all_359_1)
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | ALPHA: (253) implies:
% 28.55/4.61  | | | | | | | |   (254)  $i(all_359_1)
% 28.55/4.61  | | | | | | | |   (255)  element(all_359_1, all_114_0) = 0
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | BETA: splitting (82) gives:
% 28.55/4.61  | | | | | | | | 
% 28.55/4.61  | | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | |   (256)   ~ (all_153_1 = 0)
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | BETA: splitting (86) gives:
% 28.55/4.61  | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | |   (257)  all_155_0 = 0
% 28.55/4.61  | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | REDUCE: (84), (257) imply:
% 28.55/4.61  | | | | | | | | | |   (258)  in(all_130_2, all_114_1) = 0
% 28.55/4.61  | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | BETA: splitting (94) gives:
% 28.55/4.61  | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | |   (259)   ~ (all_161_2 = 0)
% 28.55/4.61  | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | BETA: splitting (115) gives:
% 28.55/4.61  | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | Case 1:
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | |   (260)  all_161_2 = 0
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | | REDUCE: (259), (260) imply:
% 28.55/4.61  | | | | | | | | | | | |   (261)  $false
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | Case 2:
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | |   (262)   ? [v0: any] : ( ~ (v0 = all_128_1) &
% 28.55/4.61  | | | | | | | | | | | |            set_difference(all_128_1, all_128_1) = v0 &
% 28.55/4.61  | | | | | | | | | | | |            $i(v0))
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | | DELTA: instantiating (262) with fresh symbol all_403_0
% 28.55/4.61  | | | | | | | | | | | |        gives:
% 28.55/4.61  | | | | | | | | | | | |   (263)   ~ (all_403_0 = all_128_1) &
% 28.55/4.61  | | | | | | | | | | | |          set_difference(all_128_1, all_128_1) = all_403_0 &
% 28.55/4.61  | | | | | | | | | | | |          $i(all_403_0)
% 28.55/4.61  | | | | | | | | | | | | 
% 28.55/4.61  | | | | | | | | | | | | ALPHA: (263) implies:
% 28.55/4.62  | | | | | | | | | | | |   (264)  $i(all_403_0)
% 28.55/4.62  | | | | | | | | | | | |   (265)  set_difference(all_128_1, all_128_1) = all_403_0
% 28.55/4.62  | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | BETA: splitting (112) gives:
% 28.55/4.62  | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | Case 1:
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | |   (266)  all_128_0 = empty_set
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | REDUCE: (39), (266) imply:
% 28.55/4.62  | | | | | | | | | | | | |   (267)  subset_complement(all_114_1, all_128_1) =
% 28.55/4.62  | | | | | | | | | | | | |          empty_set
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | REDUCE: (100), (266) imply:
% 28.55/4.62  | | | | | | | | | | | | |   (268)  set_difference(all_114_1, all_128_1) = empty_set
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (114) with all_130_2, simplifying
% 28.55/4.62  | | | | | | | | | | | | |              with (44), (258) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (269)   ? [v0: any] :  ? [v1: any] : (in(all_130_2,
% 28.55/4.62  | | | | | | | | | | | | |              all_128_0) = v1 & in(all_130_2, all_128_1) =
% 28.55/4.62  | | | | | | | | | | | | |            v0 & (v1 = 0 | v0 = 0))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_300_1, all_300_0,
% 28.55/4.62  | | | | | | | | | | | | |              simplifying with (239), (240) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (270)  all_300_0 = 0 |  ! [v0: $i] : ( ~ (in(all_300_1,
% 28.55/4.62  | | | | | | | | | | | | |                v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~
% 28.55/4.62  | | | | | | | | | | | | |              (v1 = 0) & in(v0, all_95_0) = v1))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (14) with empty_set, empty_set,
% 28.55/4.62  | | | | | | | | | | | | |              empty_set, simplifying with (17), (230) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (271)   ? [v0: int] : ( ~ (v0 = 0) & disjoint(empty_set,
% 28.55/4.62  | | | | | | | | | | | | |              empty_set) = v0) |  ! [v0: $i] : ( ~ (in(v0,
% 28.55/4.62  | | | | | | | | | | | | |                empty_set) = 0) |  ~ $i(v0))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_128_1, all_114_1,
% 28.55/4.62  | | | | | | | | | | | | |              simplifying with (32), (37), (233) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (272)  all_128_1 = all_114_1 |  ? [v0: int] : ( ~ (v0 =
% 28.55/4.62  | | | | | | | | | | | | |              0) & subset(all_114_1, all_128_1) = v0)
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_114_1, all_128_1,
% 28.55/4.62  | | | | | | | | | | | | |              simplifying with (32), (37), (268) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (273)  subset(all_114_1, all_128_1) = 0
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_128_1, all_128_1,
% 28.55/4.62  | | | | | | | | | | | | |              all_403_0, simplifying with (37), (264), (265)
% 28.55/4.62  | | | | | | | | | | | | |              gives:
% 28.55/4.62  | | | | | | | | | | | | |   (274)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0,
% 28.55/4.62  | | | | | | | | | | | | |                all_128_1) = v1) |  ~ $i(v0) |  ? [v2: any]
% 28.55/4.62  | | | | | | | | | | | | |            :  ? [v3: any] : (in(v0, all_403_0) = v2 &
% 28.55/4.62  | | | | | | | | | | | | |              in(v0, all_128_1) = v3 & ( ~ (v2 = 0) | (v1 =
% 28.55/4.62  | | | | | | | | | | | | |                  0 &  ~ (v3 = 0))))) &  ! [v0: $i] : ( ~
% 28.55/4.62  | | | | | | | | | | | | |            (in(v0, all_128_1) = 0) |  ~ $i(v0) |  ? [v1:
% 28.55/4.62  | | | | | | | | | | | | |              any] :  ? [v2: any] : (in(v0, all_403_0) = v2
% 28.55/4.62  | | | | | | | | | | | | |              & in(v0, all_128_1) = v1 & (v2 = 0 | v1 = 0)))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | ALPHA: (274) implies:
% 28.55/4.62  | | | | | | | | | | | | |   (275)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0,
% 28.55/4.62  | | | | | | | | | | | | |                all_128_1) = v1) |  ~ $i(v0) |  ? [v2: any]
% 28.55/4.62  | | | | | | | | | | | | |            :  ? [v3: any] : (in(v0, all_403_0) = v2 &
% 28.55/4.62  | | | | | | | | | | | | |              in(v0, all_128_1) = v3 & ( ~ (v2 = 0) | (v1 =
% 28.55/4.62  | | | | | | | | | | | | |                  0 &  ~ (v3 = 0)))))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (involutiveness_k3_subset_1) with
% 28.55/4.62  | | | | | | | | | | | | |              all_114_1, all_128_1, empty_set, all_114_1,
% 28.55/4.62  | | | | | | | | | | | | |              simplifying with (32), (37), (196), (267) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (276)  all_128_1 = all_114_1 |  ? [v0: $i] :  ? [v1: int]
% 28.55/4.62  | | | | | | | | | | | | |          : ( ~ (v1 = 0) & element(all_128_1, v0) = v1 &
% 28.55/4.62  | | | | | | | | | | | | |            powerset(all_114_1) = v0 & $i(v0))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | GROUND_INST: instantiating (275) with all_130_2, all_130_1,
% 28.55/4.62  | | | | | | | | | | | | |              simplifying with (44), (45) gives:
% 28.55/4.62  | | | | | | | | | | | | |   (277)   ? [v0: any] :  ? [v1: any] : (in(all_130_2,
% 28.55/4.62  | | | | | | | | | | | | |              all_403_0) = v0 & in(all_130_2, all_128_1) =
% 28.55/4.62  | | | | | | | | | | | | |            v1 & ( ~ (v0 = 0) | (all_130_1 = 0 &  ~ (v1 =
% 28.55/4.62  | | | | | | | | | | | | |                  0))))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | DELTA: instantiating (269) with fresh symbols all_481_0,
% 28.55/4.62  | | | | | | | | | | | | |        all_481_1 gives:
% 28.55/4.62  | | | | | | | | | | | | |   (278)  in(all_130_2, all_128_0) = all_481_0 &
% 28.55/4.62  | | | | | | | | | | | | |          in(all_130_2, all_128_1) = all_481_1 & (all_481_0
% 28.55/4.62  | | | | | | | | | | | | |            = 0 | all_481_1 = 0)
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | ALPHA: (278) implies:
% 28.55/4.62  | | | | | | | | | | | | |   (279)  in(all_130_2, all_128_1) = all_481_1
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | DELTA: instantiating (277) with fresh symbols all_502_0,
% 28.55/4.62  | | | | | | | | | | | | |        all_502_1 gives:
% 28.55/4.62  | | | | | | | | | | | | |   (280)  in(all_130_2, all_403_0) = all_502_1 &
% 28.55/4.62  | | | | | | | | | | | | |          in(all_130_2, all_128_1) = all_502_0 & ( ~
% 28.55/4.62  | | | | | | | | | | | | |            (all_502_1 = 0) | (all_130_1 = 0 &  ~ (all_502_0
% 28.55/4.62  | | | | | | | | | | | | |                = 0)))
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | ALPHA: (280) implies:
% 28.55/4.62  | | | | | | | | | | | | |   (281)  in(all_130_2, all_128_1) = all_502_0
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | BETA: splitting (276) gives:
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | Case 1:
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | |   (282)  all_128_1 = all_114_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | REDUCE: (281), (282) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (283)  in(all_130_2, all_114_1) = all_502_0
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | REDUCE: (279), (282) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (284)  in(all_130_2, all_114_1) = all_481_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | REDUCE: (45), (282) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (285)  in(all_130_2, all_114_1) = all_130_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_502_0, all_114_1,
% 28.55/4.62  | | | | | | | | | | | | | |              all_130_2, simplifying with (258), (283) gives:
% 28.55/4.62  | | | | | | | | | | | | | |   (286)  all_502_0 = 0
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_481_1, all_502_0,
% 28.55/4.62  | | | | | | | | | | | | | |              all_114_1, all_130_2, simplifying with (283),
% 28.55/4.62  | | | | | | | | | | | | | |              (284) gives:
% 28.55/4.62  | | | | | | | | | | | | | |   (287)  all_502_0 = all_481_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_130_1, all_502_0,
% 28.55/4.62  | | | | | | | | | | | | | |              all_114_1, all_130_2, simplifying with (283),
% 28.55/4.62  | | | | | | | | | | | | | |              (285) gives:
% 28.55/4.62  | | | | | | | | | | | | | |   (288)  all_502_0 = all_130_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | COMBINE_EQS: (286), (287) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (289)  all_481_1 = 0
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | COMBINE_EQS: (287), (288) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (290)  all_481_1 = all_130_1
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | COMBINE_EQS: (289), (290) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (291)  all_130_1 = 0
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | REDUCE: (42), (291) imply:
% 28.55/4.62  | | | | | | | | | | | | | |   (292)  $false
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | Case 2:
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | |   (293)   ~ (all_128_1 = all_114_1)
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | Case 1:
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | |   (294)  all_128_1 = all_114_1
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | REDUCE: (293), (294) imply:
% 28.55/4.62  | | | | | | | | | | | | | | |   (295)  $false
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent.
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | Case 2:
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | |   (296)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_114_1,
% 28.55/4.62  | | | | | | | | | | | | | | |              all_128_1) = v0)
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | Case 1:
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | |   (297)   ? [v0: int] : ( ~ (v0 = 0) & disjoint(empty_set,
% 28.55/4.62  | | | | | | | | | | | | | | | |              empty_set) = v0)
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | Case 1:
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (298)  all_300_0 = 0
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | REDUCE: (238), (298) imply:
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (299)  $false
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | Case 2:
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | DELTA: instantiating (297) with fresh symbol all_492_0
% 28.55/4.62  | | | | | | | | | | | | | | | | |        gives:
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (300)   ~ (all_492_0 = 0) & disjoint(empty_set,
% 28.55/4.62  | | | | | | | | | | | | | | | | |            empty_set) = all_492_0
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (301)   ~ (all_492_0 = 0)
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (302)  disjoint(empty_set, empty_set) = all_492_0
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_492_0, empty_set,
% 28.55/4.62  | | | | | | | | | | | | | | | | |              empty_set, simplifying with (207), (302) gives:
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (303)  all_492_0 = 0
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | REDUCE: (301), (303) imply:
% 28.55/4.62  | | | | | | | | | | | | | | | | |   (304)  $false
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent.
% 28.55/4.62  | | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | End of split
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | Case 2:
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | DELTA: instantiating (296) with fresh symbol all_536_0
% 28.55/4.62  | | | | | | | | | | | | | | | |        gives:
% 28.55/4.62  | | | | | | | | | | | | | | | |   (305)   ~ (all_536_0 = 0) & subset(all_114_1, all_128_1)
% 28.55/4.62  | | | | | | | | | | | | | | | |          = all_536_0
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 28.55/4.62  | | | | | | | | | | | | | | | |   (306)   ~ (all_536_0 = 0)
% 28.55/4.62  | | | | | | | | | | | | | | | |   (307)  subset(all_114_1, all_128_1) = all_536_0
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_536_0, all_128_1,
% 28.55/4.62  | | | | | | | | | | | | | | | |              all_114_1, simplifying with (273), (307) gives:
% 28.55/4.62  | | | | | | | | | | | | | | | |   (308)  all_536_0 = 0
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | REDUCE: (306), (308) imply:
% 28.55/4.62  | | | | | | | | | | | | | | | |   (309)  $false
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 28.55/4.62  | | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | | End of split
% 28.55/4.62  | | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | | End of split
% 28.55/4.62  | | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | | End of split
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | Case 2:
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.62  | | | | | | | | | | | | |   (310)   ~ (all_128_0 = empty_set)
% 28.55/4.62  | | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | | REF_CLOSE: (20), (42), (43), (44), (45), (46), (49), (102),
% 28.55/4.63  | | | | | | | | | | | | |            (114), (227), (258), (310) are inconsistent by
% 28.55/4.63  | | | | | | | | | | | | |            sub-proof #1.
% 28.55/4.63  | | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | Case 2:
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | |   (311)  all_161_0 = 0
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | REDUCE: (101), (311) imply:
% 28.55/4.63  | | | | | | | | | | |   (312)  subset(all_128_1, all_128_0) = 0
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | BETA: splitting (112) gives:
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | Case 1:
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | |   (313)  all_128_0 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REDUCE: (39), (313) imply:
% 28.55/4.63  | | | | | | | | | | | |   (314)  subset_complement(all_114_1, all_128_1) =
% 28.55/4.63  | | | | | | | | | | | |          empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REDUCE: (312), (313) imply:
% 28.55/4.63  | | | | | | | | | | | |   (315)  subset(all_128_1, empty_set) = 0
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_128_1, simplifying
% 28.55/4.63  | | | | | | | | | | | |              with (37), (315) gives:
% 28.55/4.63  | | | | | | | | | | | |   (316)  all_128_1 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (t43_subset_1) with all_114_1,
% 28.55/4.63  | | | | | | | | | | | |              all_359_1, all_114_0, simplifying with (32), (34),
% 28.55/4.63  | | | | | | | | | | | |              (254), (255) gives:
% 28.55/4.63  | | | | | | | | | | | |   (317)   ! [v0: $i] : ( ~ (element(v0, all_114_0) = 0) | 
% 28.55/4.63  | | | | | | | | | | | |            ~ $i(v0) |  ? [v1: any] :  ? [v2: $i] :  ? [v3:
% 28.55/4.63  | | | | | | | | | | | |              any] : (disjoint(all_359_1, v0) = v1 &
% 28.55/4.63  | | | | | | | | | | | |              subset_complement(all_114_1, v0) = v2 &
% 28.55/4.63  | | | | | | | | | | | |              subset(all_359_1, v2) = v3 & $i(v2) & ( ~ (v3
% 28.55/4.63  | | | | | | | | | | | |                  = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (317) with empty_set, simplifying
% 28.55/4.63  | | | | | | | | | | | |              with (17), (158) gives:
% 28.55/4.63  | | | | | | | | | | | |   (318)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] :
% 28.55/4.63  | | | | | | | | | | | |          (disjoint(all_359_1, empty_set) = v0 &
% 28.55/4.63  | | | | | | | | | | | |            subset_complement(all_114_1, empty_set) = v1 &
% 28.55/4.63  | | | | | | | | | | | |            subset(all_359_1, v1) = v2 & $i(v1) & ( ~ (v2 =
% 28.55/4.63  | | | | | | | | | | | |                0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (317) with all_128_1, simplifying
% 28.55/4.63  | | | | | | | | | | | |              with (37), (38) gives:
% 28.55/4.63  | | | | | | | | | | | |   (319)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] :
% 28.55/4.63  | | | | | | | | | | | |          (disjoint(all_359_1, all_128_1) = v0 &
% 28.55/4.63  | | | | | | | | | | | |            subset_complement(all_114_1, all_128_1) = v1 &
% 28.55/4.63  | | | | | | | | | | | |            subset(all_359_1, v1) = v2 & $i(v1) & ( ~ (v2 =
% 28.55/4.63  | | | | | | | | | | | |                0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_465_0,
% 28.55/4.63  | | | | | | | | | | | |        all_465_1, all_465_2 gives:
% 28.55/4.63  | | | | | | | | | | | |   (320)  disjoint(all_359_1, all_128_1) = all_465_2 &
% 28.55/4.63  | | | | | | | | | | | |          subset_complement(all_114_1, all_128_1) =
% 28.55/4.63  | | | | | | | | | | | |          all_465_1 & subset(all_359_1, all_465_1) =
% 28.55/4.63  | | | | | | | | | | | |          all_465_0 & $i(all_465_1) & ( ~ (all_465_0 = 0) |
% 28.55/4.63  | | | | | | | | | | | |            all_465_2 = 0) & ( ~ (all_465_2 = 0) | all_465_0
% 28.55/4.63  | | | | | | | | | | | |            = 0)
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | ALPHA: (320) implies:
% 28.55/4.63  | | | | | | | | | | | |   (321)  subset_complement(all_114_1, all_128_1) =
% 28.55/4.63  | | | | | | | | | | | |          all_465_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | DELTA: instantiating (318) with fresh symbols all_467_0,
% 28.55/4.63  | | | | | | | | | | | |        all_467_1, all_467_2 gives:
% 28.55/4.63  | | | | | | | | | | | |   (322)  disjoint(all_359_1, empty_set) = all_467_2 &
% 28.55/4.63  | | | | | | | | | | | |          subset_complement(all_114_1, empty_set) =
% 28.55/4.63  | | | | | | | | | | | |          all_467_1 & subset(all_359_1, all_467_1) =
% 28.55/4.63  | | | | | | | | | | | |          all_467_0 & $i(all_467_1) & ( ~ (all_467_0 = 0) |
% 28.55/4.63  | | | | | | | | | | | |            all_467_2 = 0) & ( ~ (all_467_2 = 0) | all_467_0
% 28.55/4.63  | | | | | | | | | | | |            = 0)
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | ALPHA: (322) implies:
% 28.55/4.63  | | | | | | | | | | | |   (323)  subset_complement(all_114_1, empty_set) =
% 28.55/4.63  | | | | | | | | | | | |          all_467_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REDUCE: (316), (321) imply:
% 28.55/4.63  | | | | | | | | | | | |   (324)  subset_complement(all_114_1, empty_set) =
% 28.55/4.63  | | | | | | | | | | | |          all_465_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REDUCE: (314), (316) imply:
% 28.55/4.63  | | | | | | | | | | | |   (325)  subset_complement(all_114_1, empty_set) =
% 28.55/4.63  | | | | | | | | | | | |          empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_114_1, all_467_1,
% 28.55/4.63  | | | | | | | | | | | |              empty_set, all_114_1, simplifying with (196),
% 28.55/4.63  | | | | | | | | | | | |              (323) gives:
% 28.55/4.63  | | | | | | | | | | | |   (326)  all_467_1 = all_114_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_465_1, all_467_1,
% 28.55/4.63  | | | | | | | | | | | |              empty_set, all_114_1, simplifying with (323),
% 28.55/4.63  | | | | | | | | | | | |              (324) gives:
% 28.55/4.63  | | | | | | | | | | | |   (327)  all_467_1 = all_465_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | GROUND_INST: instantiating (22) with empty_set, all_467_1,
% 28.55/4.63  | | | | | | | | | | | |              empty_set, all_114_1, simplifying with (323),
% 28.55/4.63  | | | | | | | | | | | |              (325) gives:
% 28.55/4.63  | | | | | | | | | | | |   (328)  all_467_1 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | COMBINE_EQS: (327), (328) imply:
% 28.55/4.63  | | | | | | | | | | | |   (329)  all_465_1 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply:
% 28.55/4.63  | | | | | | | | | | | |   (330)  all_465_1 = all_114_1
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | COMBINE_EQS: (329), (330) imply:
% 28.55/4.63  | | | | | | | | | | | |   (331)  all_114_1 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | SIMP: (331) implies:
% 28.55/4.63  | | | | | | | | | | | |   (332)  all_114_1 = empty_set
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REDUCE: (31), (332) imply:
% 28.55/4.63  | | | | | | | | | | | |   (333)  $false
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | Case 2:
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | |   (334)   ~ (all_128_0 = empty_set)
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | | REF_CLOSE: (20), (42), (43), (44), (45), (46), (49), (102),
% 28.55/4.63  | | | | | | | | | | | |            (114), (227), (258), (334) are inconsistent by
% 28.55/4.63  | | | | | | | | | | | |            sub-proof #1.
% 28.55/4.63  | | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | Case 2:
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | |   (335)  all_155_1 = 0
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | COMBINE_EQS: (95), (335) imply:
% 28.55/4.63  | | | | | | | | | |   (336)  all_153_1 = 0
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | REDUCE: (256), (336) imply:
% 28.55/4.63  | | | | | | | | | |   (337)  $false
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | | CLOSE: (337) is inconsistent.
% 28.55/4.63  | | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | Case 2:
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | |   (338)  all_153_1 = 0
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | REDUCE: (80), (338) imply:
% 28.55/4.63  | | | | | | | | |   (339)  empty(all_114_1) = 0
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | PRED_UNIFY: (251), (339) imply:
% 28.55/4.63  | | | | | | | | |   (340)  $false
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | | CLOSE: (340) is inconsistent.
% 28.55/4.63  | | | | | | | | | 
% 28.55/4.63  | | | | | | | | End of split
% 28.55/4.63  | | | | | | | | 
% 28.55/4.63  | | | | | | | End of split
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | End of split
% 28.55/4.63  | | | | | | 
% 28.55/4.63  | | | | | Case 2:
% 28.55/4.63  | | | | | | 
% 28.55/4.63  | | | | | |   (341)   ~ (all_194_0 = 0)
% 28.55/4.63  | | | | | | 
% 28.55/4.63  | | | | | | BETA: splitting (131) gives:
% 28.55/4.63  | | | | | | 
% 28.55/4.63  | | | | | | Case 1:
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | |   (342)   ~ (all_194_2 = 0)
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | | GROUND_INST: instantiating (23) with all_194_2, 0, empty_set,
% 28.55/4.63  | | | | | | |              all_128_1, simplifying with (150), (231) gives:
% 28.55/4.63  | | | | | | |   (343)  all_194_2 = 0
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | | REDUCE: (342), (343) imply:
% 28.55/4.63  | | | | | | |   (344)  $false
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | | CLOSE: (344) is inconsistent.
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | Case 2:
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | |   (345)  all_194_0 = 0
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | | REDUCE: (341), (345) imply:
% 28.55/4.63  | | | | | | |   (346)  $false
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | | CLOSE: (346) is inconsistent.
% 28.55/4.63  | | | | | | | 
% 28.55/4.63  | | | | | | End of split
% 28.55/4.63  | | | | | | 
% 28.55/4.63  | | | | | End of split
% 28.55/4.63  | | | | | 
% 28.55/4.63  | | | | End of split
% 28.55/4.63  | | | | 
% 28.55/4.63  | | | End of split
% 28.55/4.63  | | | 
% 28.55/4.63  | | End of split
% 28.55/4.63  | | 
% 28.55/4.63  | Case 2:
% 28.55/4.63  | | 
% 28.55/4.63  | |   (347)  all_159_1 = 0
% 28.55/4.63  | | 
% 28.55/4.63  | | COMBINE_EQS: (96), (347) imply:
% 28.55/4.63  | |   (348)  all_145_0 = 0
% 28.55/4.63  | | 
% 28.55/4.63  | | REDUCE: (65), (348) imply:
% 28.55/4.63  | |   (349)  $false
% 28.55/4.63  | | 
% 28.55/4.63  | | CLOSE: (349) is inconsistent.
% 28.55/4.63  | | 
% 28.55/4.63  | End of split
% 28.55/4.63  | 
% 28.55/4.63  End of proof
% 28.55/4.63  
% 28.55/4.63  Sub-proof #1 shows that the following formulas are inconsistent:
% 28.55/4.63  ----------------------------------------------------------------
% 28.55/4.63    (1)  $i(all_128_0)
% 28.55/4.64    (2)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (subset(v0, empty_set) = v1) | 
% 28.55/4.64           ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_95_0) = v2))
% 28.55/4.64    (3)  in(all_130_2, all_114_1) = 0
% 28.55/4.64    (4)  in(all_130_2, all_128_1) = all_130_1
% 28.55/4.64    (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 28.55/4.64         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 28.55/4.64    (6)   ~ (all_130_0 = 0)
% 28.55/4.64    (7)  in(all_130_2, all_128_0) = all_130_0
% 28.55/4.64    (8)   ~ (all_130_1 = 0)
% 28.55/4.64    (9)   ~ (all_128_0 = empty_set)
% 28.55/4.64    (10)   ! [v0: $i] : ( ~ (in(v0, all_114_1) = 0) |  ~ $i(v0) |  ? [v1: any] : 
% 28.55/4.64            ? [v2: any] : (in(v0, all_128_0) = v2 & in(v0, all_128_1) = v1 & (v2 =
% 28.55/4.64                0 | v1 = 0)))
% 28.55/4.64    (11)  $i(all_130_2)
% 28.55/4.64    (12)  all_128_0 = empty_set |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_128_0,
% 28.55/4.64              empty_set) = v0)
% 28.55/4.64  
% 28.55/4.64  Begin of proof
% 28.55/4.64  | 
% 28.55/4.64  | BETA: splitting (12) gives:
% 28.55/4.64  | 
% 28.55/4.64  | Case 1:
% 28.55/4.64  | | 
% 28.55/4.64  | |   (13)  all_128_0 = empty_set
% 28.55/4.64  | | 
% 28.55/4.64  | | REDUCE: (9), (13) imply:
% 28.55/4.64  | |   (14)  $false
% 28.55/4.64  | | 
% 28.55/4.64  | | CLOSE: (14) is inconsistent.
% 28.55/4.64  | | 
% 28.55/4.64  | Case 2:
% 28.55/4.64  | | 
% 28.55/4.64  | |   (15)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_128_0, empty_set) = v0)
% 28.55/4.64  | | 
% 28.55/4.64  | | DELTA: instantiating (15) with fresh symbol all_407_0 gives:
% 28.55/4.64  | |   (16)   ~ (all_407_0 = 0) & subset(all_128_0, empty_set) = all_407_0
% 28.55/4.64  | | 
% 28.55/4.64  | | ALPHA: (16) implies:
% 28.55/4.64  | |   (17)   ~ (all_407_0 = 0)
% 28.55/4.64  | |   (18)  subset(all_128_0, empty_set) = all_407_0
% 28.55/4.64  | | 
% 28.55/4.64  | | GROUND_INST: instantiating (10) with all_130_2, simplifying with (3), (11)
% 28.55/4.64  | |              gives:
% 28.55/4.64  | |   (19)   ? [v0: any] :  ? [v1: any] : (in(all_130_2, all_128_0) = v1 &
% 28.55/4.64  | |           in(all_130_2, all_128_1) = v0 & (v1 = 0 | v0 = 0))
% 28.55/4.64  | | 
% 28.55/4.64  | | GROUND_INST: instantiating (2) with all_128_0, all_407_0, simplifying with
% 28.55/4.64  | |              (1), (18) gives:
% 28.55/4.64  | |   (20)  all_407_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_128_0,
% 28.55/4.64  | |             all_95_0) = v0)
% 28.55/4.64  | | 
% 28.55/4.64  | | DELTA: instantiating (19) with fresh symbols all_454_0, all_454_1 gives:
% 28.55/4.64  | |   (21)  in(all_130_2, all_128_0) = all_454_0 & in(all_130_2, all_128_1) =
% 28.55/4.64  | |         all_454_1 & (all_454_0 = 0 | all_454_1 = 0)
% 28.55/4.64  | | 
% 28.55/4.64  | | ALPHA: (21) implies:
% 28.55/4.64  | |   (22)  in(all_130_2, all_128_1) = all_454_1
% 28.55/4.64  | |   (23)  in(all_130_2, all_128_0) = all_454_0
% 28.55/4.64  | |   (24)  all_454_0 = 0 | all_454_1 = 0
% 28.55/4.64  | | 
% 28.55/4.64  | | BETA: splitting (20) gives:
% 28.55/4.64  | | 
% 28.55/4.64  | | Case 1:
% 28.55/4.64  | | | 
% 28.55/4.64  | | |   (25)  all_407_0 = 0
% 28.55/4.64  | | | 
% 28.55/4.64  | | | REDUCE: (17), (25) imply:
% 28.55/4.64  | | |   (26)  $false
% 28.55/4.64  | | | 
% 28.55/4.64  | | | CLOSE: (26) is inconsistent.
% 28.55/4.64  | | | 
% 28.55/4.64  | | Case 2:
% 28.55/4.64  | | | 
% 28.55/4.64  | | | 
% 28.55/4.64  | | | GROUND_INST: instantiating (5) with all_130_1, all_454_1, all_128_1,
% 28.55/4.64  | | |              all_130_2, simplifying with (4), (22) gives:
% 28.55/4.64  | | |   (27)  all_454_1 = all_130_1
% 28.55/4.64  | | | 
% 28.55/4.64  | | | GROUND_INST: instantiating (5) with all_130_0, all_454_0, all_128_0,
% 28.55/4.64  | | |              all_130_2, simplifying with (7), (23) gives:
% 28.55/4.64  | | |   (28)  all_454_0 = all_130_0
% 28.55/4.64  | | | 
% 28.55/4.64  | | | BETA: splitting (24) gives:
% 28.55/4.64  | | | 
% 28.55/4.64  | | | Case 1:
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | |   (29)  all_454_0 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | COMBINE_EQS: (28), (29) imply:
% 28.55/4.64  | | | |   (30)  all_130_0 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | SIMP: (30) implies:
% 28.55/4.64  | | | |   (31)  all_130_0 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | REDUCE: (6), (31) imply:
% 28.55/4.64  | | | |   (32)  $false
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | CLOSE: (32) is inconsistent.
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | Case 2:
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | |   (33)  all_454_1 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | COMBINE_EQS: (27), (33) imply:
% 28.55/4.64  | | | |   (34)  all_130_1 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | SIMP: (34) implies:
% 28.55/4.64  | | | |   (35)  all_130_1 = 0
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | REDUCE: (8), (35) imply:
% 28.55/4.64  | | | |   (36)  $false
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | | CLOSE: (36) is inconsistent.
% 28.55/4.64  | | | | 
% 28.55/4.64  | | | End of split
% 28.55/4.64  | | | 
% 28.55/4.64  | | End of split
% 28.55/4.64  | | 
% 28.55/4.64  | End of split
% 28.55/4.64  | 
% 28.55/4.64  End of proof
% 28.55/4.64  % SZS output end Proof for theBenchmark
% 28.55/4.64  
% 28.55/4.64  3979ms
%------------------------------------------------------------------------------