TSTP Solution File: SEU125+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU125+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:42:37 EDT 2023

% Result   : Theorem 6.17s 1.60s
% Output   : Proof 8.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU125+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 18:07:06 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/1.03  Prover 4: Preprocessing ...
% 2.12/1.03  Prover 1: Preprocessing ...
% 2.63/1.08  Prover 6: Preprocessing ...
% 2.63/1.08  Prover 5: Preprocessing ...
% 2.63/1.08  Prover 0: Preprocessing ...
% 2.63/1.08  Prover 2: Preprocessing ...
% 2.63/1.08  Prover 3: Preprocessing ...
% 3.64/1.40  Prover 1: Warning: ignoring some quantifiers
% 3.64/1.40  Prover 4: Warning: ignoring some quantifiers
% 3.64/1.40  Prover 3: Warning: ignoring some quantifiers
% 3.64/1.41  Prover 2: Proving ...
% 3.64/1.41  Prover 5: Proving ...
% 4.65/1.42  Prover 6: Proving ...
% 4.65/1.42  Prover 4: Constructing countermodel ...
% 4.65/1.42  Prover 3: Constructing countermodel ...
% 4.65/1.42  Prover 1: Constructing countermodel ...
% 4.65/1.43  Prover 0: Proving ...
% 6.17/1.60  Prover 0: proved (985ms)
% 6.17/1.60  
% 6.17/1.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.60  
% 6.17/1.60  Prover 6: stopped
% 6.28/1.61  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.28/1.61  Prover 5: stopped
% 6.32/1.61  Prover 3: stopped
% 6.32/1.61  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.32/1.61  Prover 2: stopped
% 6.32/1.62  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.32/1.62  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.32/1.62  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.32/1.65  Prover 8: Preprocessing ...
% 6.32/1.65  Prover 7: Preprocessing ...
% 6.32/1.65  Prover 11: Preprocessing ...
% 6.32/1.65  Prover 13: Preprocessing ...
% 6.32/1.65  Prover 10: Preprocessing ...
% 6.32/1.70  Prover 10: Warning: ignoring some quantifiers
% 6.95/1.70  Prover 10: Constructing countermodel ...
% 6.95/1.71  Prover 7: Warning: ignoring some quantifiers
% 6.95/1.71  Prover 7: Constructing countermodel ...
% 6.95/1.72  Prover 8: Warning: ignoring some quantifiers
% 6.95/1.72  Prover 13: Warning: ignoring some quantifiers
% 6.95/1.72  Prover 13: Constructing countermodel ...
% 6.95/1.72  Prover 8: Constructing countermodel ...
% 6.95/1.72  Prover 1: gave up
% 6.95/1.74  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.95/1.76  Prover 16: Preprocessing ...
% 6.95/1.77  Prover 11: Warning: ignoring some quantifiers
% 6.95/1.77  Prover 11: Constructing countermodel ...
% 7.56/1.79  Prover 10: gave up
% 7.56/1.79  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.56/1.80  Prover 13: gave up
% 7.56/1.80  Prover 4: Found proof (size 50)
% 7.56/1.80  Prover 4: proved (1182ms)
% 7.56/1.80  Prover 11: stopped
% 7.56/1.80  Prover 8: stopped
% 7.56/1.81  Prover 7: stopped
% 7.56/1.81  Prover 16: Warning: ignoring some quantifiers
% 7.56/1.82  Prover 19: Preprocessing ...
% 7.56/1.82  Prover 16: Constructing countermodel ...
% 7.56/1.82  Prover 16: stopped
% 7.56/1.87  Prover 19: Warning: ignoring some quantifiers
% 7.56/1.87  Prover 19: Constructing countermodel ...
% 7.56/1.88  Prover 19: stopped
% 7.56/1.88  
% 7.56/1.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.56/1.88  
% 8.11/1.89  % SZS output start Proof for theBenchmark
% 8.11/1.89  Assumptions after simplification:
% 8.11/1.89  ---------------------------------
% 8.11/1.89  
% 8.11/1.89    (commutativity_k2_xboole_0)
% 8.18/1.92     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) |  ~
% 8.18/1.92      $i(v1) |  ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) &  ! [v0: $i] :  !
% 8.18/1.92    [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.18/1.92      | (set_union2(v1, v0) = v2 & $i(v2)))
% 8.18/1.92  
% 8.18/1.92    (d2_xboole_0)
% 8.18/1.94     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 8.18/1.94      |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ~ $i(v3) |  ~
% 8.18/1.94      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] : ( ~ (v6 = 0)
% 8.18/1.94        &  ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) &  ! [v0: $i] :  !
% 8.18/1.94    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0 |  ~
% 8.18/1.94      (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ~ $i(v3) |  ~ $i(v2) | 
% 8.18/1.94      ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) = v5 &
% 8.18/1.94        in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0: $i] :  ! [v1: $i] : 
% 8.18/1.94    ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0 |  ~ (set_union2(v0, v1) =
% 8.18/1.94        v2) |  ~ (in(v3, v0) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.18/1.94      |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 8.18/1.94            = 0) | v6 = 0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 8.18/1.94      $i] :  ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) | 
% 8.18/1.94      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :
% 8.18/1.94      (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 =
% 8.18/1.94              0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  !
% 8.18/1.94    [v4: any] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ~ $i(v3) |
% 8.18/1.94       ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3,
% 8.18/1.94          v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 = 0))))) & 
% 8.18/1.94    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 8.18/1.94        = v2) |  ~ (in(v3, v2) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.18/1.94      $i(v0) |  ? [v4: any] :  ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 8.18/1.94        (v5 = 0 | v4 = 0))) &  ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 8.18/1.94      $i] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.18/1.94      $i(v0) |  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] :  ? [v7: any] : (in(v4,
% 8.18/1.94          v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 8.18/1.94            ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 8.18/1.94  
% 8.18/1.94    (d3_tarski)
% 8.18/1.94     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 8.18/1.94      (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.18/1.95      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0: $i] :  !
% 8.18/1.95    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) |  ~
% 8.18/1.95      $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 8.18/1.95        in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 8.18/1.95      (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.18/1.95      $i(v0) | in(v2, v1) = 0)
% 8.18/1.95  
% 8.18/1.95    (t8_xboole_1)
% 8.18/1.95     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] : ( ~ (v4
% 8.18/1.95        = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 &
% 8.18/1.95      set_union2(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.18/1.95  
% 8.18/1.95    (function-axioms)
% 8.18/1.95     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 8.18/1.95    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 8.18/1.95    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.18/1.95      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0:
% 8.18/1.95      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 8.18/1.95    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 8.18/1.95      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 8.18/1.95      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 8.18/1.95  
% 8.18/1.95  Further assumptions not needed in the proof:
% 8.18/1.95  --------------------------------------------
% 8.18/1.95  antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k2_xboole_0, fc1_xboole_0,
% 8.18/1.95  fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 8.18/1.95  reflexivity_r1_tarski, t1_boole, t6_boole, t7_boole, t8_boole
% 8.18/1.95  
% 8.18/1.95  Those formulas are unsatisfiable:
% 8.18/1.95  ---------------------------------
% 8.18/1.95  
% 8.18/1.95  Begin of proof
% 8.18/1.95  | 
% 8.18/1.95  | ALPHA: (commutativity_k2_xboole_0) implies:
% 8.18/1.95  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 8.18/1.95  |          |  ~ $i(v1) |  ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 8.18/1.95  | 
% 8.18/1.95  | ALPHA: (d2_xboole_0) implies:
% 8.18/1.95  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.18/1.95  |          (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ~ $i(v3) |  ~
% 8.18/1.95  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :
% 8.18/1.95  |          (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 8.18/1.95  | 
% 8.18/1.95  | ALPHA: (d3_tarski) implies:
% 8.18/1.96  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 8.18/1.96  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 8.18/1.96  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.18/1.96  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 8.18/1.96  |          (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |
% 8.18/1.96  |           ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 8.18/1.96  | 
% 8.18/1.96  | ALPHA: (function-axioms) implies:
% 8.18/1.96  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.18/1.96  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 8.18/1.96  | 
% 8.18/1.96  | DELTA: instantiating (t8_xboole_1) with fresh symbols all_20_0, all_20_1,
% 8.18/1.96  |        all_20_2, all_20_3, all_20_4 gives:
% 8.18/1.96  |   (6)   ~ (all_20_0 = 0) & subset(all_20_1, all_20_3) = all_20_0 &
% 8.18/1.96  |        subset(all_20_2, all_20_3) = 0 & subset(all_20_4, all_20_3) = 0 &
% 8.18/1.96  |        set_union2(all_20_4, all_20_2) = all_20_1 & $i(all_20_1) & $i(all_20_2)
% 8.18/1.96  |        & $i(all_20_3) & $i(all_20_4)
% 8.18/1.96  | 
% 8.18/1.96  | ALPHA: (6) implies:
% 8.18/1.96  |   (7)   ~ (all_20_0 = 0)
% 8.18/1.96  |   (8)  $i(all_20_4)
% 8.18/1.96  |   (9)  $i(all_20_3)
% 8.18/1.96  |   (10)  $i(all_20_2)
% 8.18/1.96  |   (11)  set_union2(all_20_4, all_20_2) = all_20_1
% 8.18/1.96  |   (12)  subset(all_20_4, all_20_3) = 0
% 8.18/1.96  |   (13)  subset(all_20_2, all_20_3) = 0
% 8.18/1.96  |   (14)  subset(all_20_1, all_20_3) = all_20_0
% 8.18/1.96  | 
% 8.18/1.96  | GROUND_INST: instantiating (1) with all_20_2, all_20_4, all_20_1, simplifying
% 8.18/1.96  |              with (8), (10), (11) gives:
% 8.18/1.96  |   (15)  set_union2(all_20_2, all_20_4) = all_20_1 & $i(all_20_1)
% 8.18/1.96  | 
% 8.18/1.96  | ALPHA: (15) implies:
% 8.18/1.96  |   (16)  $i(all_20_1)
% 8.18/1.96  |   (17)  set_union2(all_20_2, all_20_4) = all_20_1
% 8.18/1.96  | 
% 8.18/1.96  | GROUND_INST: instantiating (3) with all_20_1, all_20_3, all_20_0, simplifying
% 8.18/1.96  |              with (9), (14), (16) gives:
% 8.18/1.96  |   (18)  all_20_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.18/1.96  |             all_20_1) = 0 & in(v0, all_20_3) = v1 & $i(v0))
% 8.18/1.96  | 
% 8.18/1.96  | BETA: splitting (18) gives:
% 8.18/1.96  | 
% 8.18/1.97  | Case 1:
% 8.18/1.97  | | 
% 8.18/1.97  | |   (19)  all_20_0 = 0
% 8.18/1.97  | | 
% 8.18/1.97  | | REDUCE: (7), (19) imply:
% 8.18/1.97  | |   (20)  $false
% 8.18/1.97  | | 
% 8.18/1.97  | | CLOSE: (20) is inconsistent.
% 8.18/1.97  | | 
% 8.18/1.97  | Case 2:
% 8.18/1.97  | | 
% 8.18/1.97  | |   (21)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_1) = 0 &
% 8.18/1.97  | |           in(v0, all_20_3) = v1 & $i(v0))
% 8.18/1.97  | | 
% 8.18/1.97  | | DELTA: instantiating (21) with fresh symbols all_38_0, all_38_1 gives:
% 8.18/1.97  | |   (22)   ~ (all_38_0 = 0) & in(all_38_1, all_20_1) = 0 & in(all_38_1,
% 8.18/1.97  | |           all_20_3) = all_38_0 & $i(all_38_1)
% 8.18/1.97  | | 
% 8.18/1.97  | | ALPHA: (22) implies:
% 8.18/1.97  | |   (23)   ~ (all_38_0 = 0)
% 8.18/1.97  | |   (24)  $i(all_38_1)
% 8.18/1.97  | |   (25)  in(all_38_1, all_20_3) = all_38_0
% 8.18/1.97  | |   (26)  in(all_38_1, all_20_1) = 0
% 8.18/1.97  | | 
% 8.18/1.97  | | GROUND_INST: instantiating (4) with all_20_2, all_20_3, all_38_1, all_38_0,
% 8.18/1.97  | |              simplifying with (9), (10), (13), (24), (25) gives:
% 8.18/1.97  | |   (27)  all_38_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2)
% 8.18/1.97  | |           = v0)
% 8.18/1.97  | | 
% 8.18/1.97  | | GROUND_INST: instantiating (4) with all_20_4, all_20_3, all_38_1, all_38_0,
% 8.18/1.97  | |              simplifying with (8), (9), (12), (24), (25) gives:
% 8.18/1.97  | |   (28)  all_38_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4)
% 8.18/1.97  | |           = v0)
% 8.18/1.97  | | 
% 8.18/1.97  | | GROUND_INST: instantiating (2) with all_20_4, all_20_2, all_20_1, all_38_1,
% 8.18/1.97  | |              simplifying with (8), (10), (11), (16), (24), (26) gives:
% 8.18/1.97  | |   (29)   ? [v0: any] :  ? [v1: any] : (in(all_38_1, all_20_2) = v1 &
% 8.18/1.97  | |           in(all_38_1, all_20_4) = v0 & (v1 = 0 | v0 = 0))
% 8.18/1.97  | | 
% 8.18/1.97  | | GROUND_INST: instantiating (2) with all_20_2, all_20_4, all_20_1, all_38_1,
% 8.18/1.97  | |              simplifying with (8), (10), (16), (17), (24), (26) gives:
% 8.18/1.98  | |   (30)   ? [v0: any] :  ? [v1: any] : (in(all_38_1, all_20_2) = v0 &
% 8.18/1.98  | |           in(all_38_1, all_20_4) = v1 & (v1 = 0 | v0 = 0))
% 8.18/1.98  | | 
% 8.18/1.98  | | DELTA: instantiating (29) with fresh symbols all_55_0, all_55_1 gives:
% 8.18/1.98  | |   (31)  in(all_38_1, all_20_2) = all_55_0 & in(all_38_1, all_20_4) =
% 8.18/1.98  | |         all_55_1 & (all_55_0 = 0 | all_55_1 = 0)
% 8.18/1.98  | | 
% 8.18/1.98  | | ALPHA: (31) implies:
% 8.18/1.98  | |   (32)  in(all_38_1, all_20_4) = all_55_1
% 8.18/1.98  | |   (33)  in(all_38_1, all_20_2) = all_55_0
% 8.18/1.98  | | 
% 8.18/1.98  | | DELTA: instantiating (30) with fresh symbols all_59_0, all_59_1 gives:
% 8.18/1.98  | |   (34)  in(all_38_1, all_20_2) = all_59_1 & in(all_38_1, all_20_4) =
% 8.18/1.98  | |         all_59_0 & (all_59_0 = 0 | all_59_1 = 0)
% 8.18/1.98  | | 
% 8.18/1.98  | | ALPHA: (34) implies:
% 8.18/1.98  | |   (35)  in(all_38_1, all_20_4) = all_59_0
% 8.18/1.98  | |   (36)  in(all_38_1, all_20_2) = all_59_1
% 8.18/1.98  | |   (37)  all_59_0 = 0 | all_59_1 = 0
% 8.18/1.98  | | 
% 8.18/1.98  | | BETA: splitting (28) gives:
% 8.18/1.98  | | 
% 8.18/1.98  | | Case 1:
% 8.18/1.98  | | | 
% 8.18/1.98  | | |   (38)  all_38_0 = 0
% 8.18/1.98  | | | 
% 8.18/1.98  | | | REDUCE: (23), (38) imply:
% 8.18/1.98  | | |   (39)  $false
% 8.18/1.98  | | | 
% 8.18/1.98  | | | CLOSE: (39) is inconsistent.
% 8.18/1.98  | | | 
% 8.18/1.98  | | Case 2:
% 8.18/1.98  | | | 
% 8.18/1.98  | | |   (40)   ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4) = v0)
% 8.18/1.98  | | | 
% 8.18/1.98  | | | DELTA: instantiating (40) with fresh symbol all_65_0 gives:
% 8.18/1.98  | | |   (41)   ~ (all_65_0 = 0) & in(all_38_1, all_20_4) = all_65_0
% 8.18/1.98  | | | 
% 8.18/1.98  | | | ALPHA: (41) implies:
% 8.18/1.98  | | |   (42)   ~ (all_65_0 = 0)
% 8.18/1.98  | | |   (43)  in(all_38_1, all_20_4) = all_65_0
% 8.18/1.98  | | | 
% 8.18/1.98  | | | BETA: splitting (27) gives:
% 8.18/1.98  | | | 
% 8.18/1.98  | | | Case 1:
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | |   (44)  all_38_0 = 0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | REDUCE: (23), (44) imply:
% 8.18/1.98  | | | |   (45)  $false
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | CLOSE: (45) is inconsistent.
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | Case 2:
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | |   (46)   ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2) = v0)
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | DELTA: instantiating (46) with fresh symbol all_71_0 gives:
% 8.18/1.98  | | | |   (47)   ~ (all_71_0 = 0) & in(all_38_1, all_20_2) = all_71_0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | ALPHA: (47) implies:
% 8.18/1.98  | | | |   (48)   ~ (all_71_0 = 0)
% 8.18/1.98  | | | |   (49)  in(all_38_1, all_20_2) = all_71_0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | GROUND_INST: instantiating (5) with all_59_0, all_65_0, all_20_4,
% 8.18/1.98  | | | |              all_38_1, simplifying with (35), (43) gives:
% 8.18/1.98  | | | |   (50)  all_65_0 = all_59_0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | GROUND_INST: instantiating (5) with all_55_1, all_65_0, all_20_4,
% 8.18/1.98  | | | |              all_38_1, simplifying with (32), (43) gives:
% 8.18/1.98  | | | |   (51)  all_65_0 = all_55_1
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | GROUND_INST: instantiating (5) with all_59_1, all_71_0, all_20_2,
% 8.18/1.98  | | | |              all_38_1, simplifying with (36), (49) gives:
% 8.18/1.98  | | | |   (52)  all_71_0 = all_59_1
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | GROUND_INST: instantiating (5) with all_55_0, all_71_0, all_20_2,
% 8.18/1.98  | | | |              all_38_1, simplifying with (33), (49) gives:
% 8.18/1.98  | | | |   (53)  all_71_0 = all_55_0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | COMBINE_EQS: (52), (53) imply:
% 8.18/1.98  | | | |   (54)  all_59_1 = all_55_0
% 8.18/1.98  | | | | 
% 8.18/1.98  | | | | SIMP: (54) implies:
% 8.18/1.99  | | | |   (55)  all_59_1 = all_55_0
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | | COMBINE_EQS: (50), (51) imply:
% 8.18/1.99  | | | |   (56)  all_59_0 = all_55_1
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | | REDUCE: (48), (53) imply:
% 8.18/1.99  | | | |   (57)   ~ (all_55_0 = 0)
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | | REDUCE: (42), (51) imply:
% 8.18/1.99  | | | |   (58)   ~ (all_55_1 = 0)
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | | BETA: splitting (37) gives:
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | | Case 1:
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | |   (59)  all_59_0 = 0
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | COMBINE_EQS: (56), (59) imply:
% 8.18/1.99  | | | | |   (60)  all_55_1 = 0
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | SIMP: (60) implies:
% 8.18/1.99  | | | | |   (61)  all_55_1 = 0
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | REDUCE: (58), (61) imply:
% 8.18/1.99  | | | | |   (62)  $false
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | CLOSE: (62) is inconsistent.
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | Case 2:
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | |   (63)  all_59_1 = 0
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | COMBINE_EQS: (55), (63) imply:
% 8.18/1.99  | | | | |   (64)  all_55_0 = 0
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | REDUCE: (57), (64) imply:
% 8.18/1.99  | | | | |   (65)  $false
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | | CLOSE: (65) is inconsistent.
% 8.18/1.99  | | | | | 
% 8.18/1.99  | | | | End of split
% 8.18/1.99  | | | | 
% 8.18/1.99  | | | End of split
% 8.18/1.99  | | | 
% 8.18/1.99  | | End of split
% 8.18/1.99  | | 
% 8.18/1.99  | End of split
% 8.18/1.99  | 
% 8.18/1.99  End of proof
% 8.18/1.99  % SZS output end Proof for theBenchmark
% 8.18/1.99  
% 8.18/1.99  1389ms
%------------------------------------------------------------------------------