TSTP Solution File: SEU128+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU128+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 : n023.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 17:42:38 EDT 2023

% Result   : Theorem 5.71s 1.52s
% Output   : Proof 6.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU128+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n023.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 19:14:57 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.61  Running up to 7 provers in parallel.
% 0.71/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.88/1.00  Prover 4: Preprocessing ...
% 1.88/1.00  Prover 1: Preprocessing ...
% 2.38/1.05  Prover 3: Preprocessing ...
% 2.38/1.05  Prover 0: Preprocessing ...
% 2.38/1.05  Prover 5: Preprocessing ...
% 2.38/1.05  Prover 6: Preprocessing ...
% 2.38/1.06  Prover 2: Preprocessing ...
% 3.94/1.29  Prover 5: Proving ...
% 4.40/1.31  Prover 1: Warning: ignoring some quantifiers
% 4.40/1.32  Prover 2: Proving ...
% 4.40/1.32  Prover 3: Warning: ignoring some quantifiers
% 4.40/1.32  Prover 6: Proving ...
% 4.40/1.33  Prover 3: Constructing countermodel ...
% 4.40/1.33  Prover 4: Warning: ignoring some quantifiers
% 4.40/1.34  Prover 1: Constructing countermodel ...
% 4.40/1.35  Prover 4: Constructing countermodel ...
% 4.40/1.35  Prover 0: Proving ...
% 5.71/1.52  Prover 0: proved (903ms)
% 5.71/1.52  
% 5.71/1.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.71/1.52  
% 5.71/1.53  Prover 3: stopped
% 5.71/1.53  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.71/1.53  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.71/1.53  Prover 5: stopped
% 5.71/1.53  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.71/1.53  Prover 2: stopped
% 6.08/1.54  Prover 6: stopped
% 6.08/1.54  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.08/1.54  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.08/1.56  Prover 7: Preprocessing ...
% 6.08/1.56  Prover 10: Preprocessing ...
% 6.08/1.57  Prover 13: Preprocessing ...
% 6.08/1.57  Prover 4: Found proof (size 30)
% 6.08/1.57  Prover 11: Preprocessing ...
% 6.08/1.57  Prover 4: proved (944ms)
% 6.08/1.57  Prover 1: stopped
% 6.08/1.57  Prover 8: Preprocessing ...
% 6.08/1.59  Prover 10: stopped
% 6.08/1.59  Prover 7: stopped
% 6.08/1.59  Prover 13: stopped
% 6.08/1.59  Prover 11: stopped
% 6.51/1.63  Prover 8: Warning: ignoring some quantifiers
% 6.51/1.64  Prover 8: Constructing countermodel ...
% 6.51/1.65  Prover 8: stopped
% 6.51/1.65  
% 6.51/1.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.51/1.65  
% 6.51/1.66  % SZS output start Proof for theBenchmark
% 6.51/1.66  Assumptions after simplification:
% 6.51/1.66  ---------------------------------
% 6.51/1.66  
% 6.51/1.66    (commutativity_k3_xboole_0)
% 6.81/1.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 6.81/1.69      |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) &  !
% 6.81/1.69    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | 
% 6.81/1.69      ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 6.81/1.69  
% 6.81/1.69    (d3_tarski)
% 6.81/1.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.81/1.70      (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.81/1.70      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0: $i] :  !
% 6.81/1.70    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) |  ~
% 6.81/1.70      $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.81/1.70        in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 6.81/1.70      (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.81/1.70      $i(v0) | in(v2, v1) = 0)
% 6.81/1.70  
% 6.81/1.70    (d3_xboole_0)
% 6.81/1.71     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 6.81/1.71      |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ~ $i(v3) | 
% 6.81/1.71      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v1)
% 6.81/1.71        = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0: $i] :  !
% 6.81/1.71    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: any] : ( ~
% 6.81/1.71      (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ~ $i(v3) |  ~
% 6.81/1.71      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) =
% 6.81/1.71        v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0: $i] :
% 6.81/1.71     ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: any] : ( ~
% 6.81/1.71      (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ~ $i(v3) |  ~
% 6.81/1.71      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) =
% 6.81/1.71        v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0: $i] :
% 6.81/1.71     ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 6.81/1.71      |  ~ (in(v3, v2) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 6.81/1.71      (in(v3, v1) = 0 & in(v3, v0) = 0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 6.81/1.71    :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = 0) | 
% 6.81/1.71      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :
% 6.81/1.71      (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v0: $i]
% 6.81/1.71    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 6.81/1.71        v2) |  ~ (in(v3, v0) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 6.81/1.71      |  ? [v4: any] :  ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 6.81/1.71            = 0) | v5 = 0))) &  ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 6.81/1.71      $i] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1)
% 6.81/1.71      |  ~ $i(v0) |  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] :  ? [v7: any] :
% 6.81/1.71      (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 6.81/1.72          |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 6.81/1.72  
% 6.81/1.72    (t19_xboole_1)
% 6.81/1.72     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] : ( ~ (v4
% 6.81/1.72        = 0) & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 &
% 6.81/1.72      set_intersection2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.81/1.72  
% 6.81/1.72    (function-axioms)
% 6.81/1.72     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 6.81/1.72    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 6.81/1.72    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.81/1.72      (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  !
% 6.81/1.72    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 6.81/1.72      $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 6.81/1.72      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 6.81/1.72      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 6.81/1.72  
% 6.81/1.72  Further assumptions not needed in the proof:
% 6.81/1.72  --------------------------------------------
% 6.81/1.72  antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 6.81/1.72  idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 6.81/1.72  t2_boole, t6_boole, t7_boole, t8_boole
% 6.81/1.72  
% 6.81/1.72  Those formulas are unsatisfiable:
% 6.81/1.72  ---------------------------------
% 6.81/1.72  
% 6.81/1.72  Begin of proof
% 6.81/1.72  | 
% 6.81/1.72  | ALPHA: (commutativity_k3_xboole_0) implies:
% 6.81/1.72  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1,
% 6.81/1.72  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) =
% 6.81/1.72  |            v2 & $i(v2)))
% 6.81/1.72  | 
% 6.81/1.72  | ALPHA: (d3_tarski) implies:
% 6.81/1.72  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (subset(v0, v1) = 0) |  ~
% 6.81/1.72  |          (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | in(v2, v1) =
% 6.81/1.72  |          0)
% 6.81/1.72  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 6.81/1.72  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 6.81/1.72  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.81/1.72  | 
% 6.81/1.72  | ALPHA: (d3_xboole_0) implies:
% 6.81/1.73  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 6.81/1.73  |        (v4 = 0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) | 
% 6.81/1.73  |          ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6:
% 6.81/1.73  |            any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 =
% 6.81/1.73  |                0))))
% 6.81/1.73  | 
% 6.81/1.73  | ALPHA: (function-axioms) implies:
% 6.81/1.73  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.81/1.73  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.81/1.73  | 
% 6.81/1.73  | DELTA: instantiating (t19_xboole_1) with fresh symbols all_18_0, all_18_1,
% 6.81/1.73  |        all_18_2, all_18_3, all_18_4 gives:
% 6.81/1.73  |   (6)   ~ (all_18_0 = 0) & subset(all_18_4, all_18_1) = all_18_0 &
% 6.81/1.73  |        subset(all_18_4, all_18_2) = 0 & subset(all_18_4, all_18_3) = 0 &
% 6.81/1.73  |        set_intersection2(all_18_3, all_18_2) = all_18_1 & $i(all_18_1) &
% 6.81/1.73  |        $i(all_18_2) & $i(all_18_3) & $i(all_18_4)
% 6.81/1.73  | 
% 6.81/1.73  | ALPHA: (6) implies:
% 6.81/1.73  |   (7)   ~ (all_18_0 = 0)
% 6.81/1.73  |   (8)  $i(all_18_4)
% 6.81/1.73  |   (9)  $i(all_18_3)
% 6.81/1.73  |   (10)  $i(all_18_2)
% 6.81/1.73  |   (11)  set_intersection2(all_18_3, all_18_2) = all_18_1
% 6.81/1.73  |   (12)  subset(all_18_4, all_18_3) = 0
% 6.81/1.73  |   (13)  subset(all_18_4, all_18_2) = 0
% 6.81/1.73  |   (14)  subset(all_18_4, all_18_1) = all_18_0
% 6.81/1.73  | 
% 6.81/1.73  | GROUND_INST: instantiating (1) with all_18_2, all_18_3, all_18_1, simplifying
% 6.81/1.73  |              with (9), (10), (11) gives:
% 6.81/1.73  |   (15)  set_intersection2(all_18_2, all_18_3) = all_18_1 & $i(all_18_1)
% 6.81/1.73  | 
% 6.81/1.73  | ALPHA: (15) implies:
% 6.81/1.73  |   (16)  $i(all_18_1)
% 6.81/1.73  | 
% 6.81/1.73  | GROUND_INST: instantiating (3) with all_18_4, all_18_1, all_18_0, simplifying
% 6.81/1.73  |              with (8), (14), (16) gives:
% 6.81/1.73  |   (17)  all_18_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.81/1.73  |             all_18_1) = v1 & in(v0, all_18_4) = 0 & $i(v0))
% 6.81/1.73  | 
% 6.81/1.73  | BETA: splitting (17) gives:
% 6.81/1.73  | 
% 6.81/1.73  | Case 1:
% 6.81/1.73  | | 
% 6.81/1.73  | |   (18)  all_18_0 = 0
% 6.81/1.73  | | 
% 6.81/1.73  | | REDUCE: (7), (18) imply:
% 6.81/1.73  | |   (19)  $false
% 6.81/1.74  | | 
% 6.81/1.74  | | CLOSE: (19) is inconsistent.
% 6.81/1.74  | | 
% 6.81/1.74  | Case 2:
% 6.81/1.74  | | 
% 6.81/1.74  | |   (20)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = v1 &
% 6.81/1.74  | |           in(v0, all_18_4) = 0 & $i(v0))
% 6.81/1.74  | | 
% 6.81/1.74  | | DELTA: instantiating (20) with fresh symbols all_32_0, all_32_1 gives:
% 6.81/1.74  | |   (21)   ~ (all_32_0 = 0) & in(all_32_1, all_18_1) = all_32_0 & in(all_32_1,
% 6.81/1.74  | |           all_18_4) = 0 & $i(all_32_1)
% 6.81/1.74  | | 
% 6.81/1.74  | | ALPHA: (21) implies:
% 6.81/1.74  | |   (22)   ~ (all_32_0 = 0)
% 6.81/1.74  | |   (23)  $i(all_32_1)
% 6.81/1.74  | |   (24)  in(all_32_1, all_18_4) = 0
% 6.81/1.74  | |   (25)  in(all_32_1, all_18_1) = all_32_0
% 6.81/1.74  | | 
% 6.81/1.74  | | GROUND_INST: instantiating (2) with all_18_4, all_18_2, all_32_1,
% 6.81/1.74  | |              simplifying with (8), (10), (13), (23), (24) gives:
% 6.81/1.74  | |   (26)  in(all_32_1, all_18_2) = 0
% 6.81/1.74  | | 
% 6.81/1.74  | | GROUND_INST: instantiating (2) with all_18_4, all_18_3, all_32_1,
% 6.81/1.74  | |              simplifying with (8), (9), (12), (23), (24) gives:
% 6.81/1.74  | |   (27)  in(all_32_1, all_18_3) = 0
% 6.81/1.74  | | 
% 6.81/1.74  | | GROUND_INST: instantiating (4) with all_18_3, all_18_2, all_18_1, all_32_1,
% 6.81/1.74  | |              all_32_0, simplifying with (9), (10), (11), (16), (23), (25)
% 6.81/1.74  | |              gives:
% 6.81/1.74  | |   (28)  all_32_0 = 0 |  ? [v0: any] :  ? [v1: any] : (in(all_32_1, all_18_2)
% 6.81/1.74  | |           = v1 & in(all_32_1, all_18_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.81/1.74  | | 
% 6.81/1.74  | | BETA: splitting (28) gives:
% 6.81/1.74  | | 
% 6.81/1.74  | | Case 1:
% 6.81/1.74  | | | 
% 6.81/1.74  | | |   (29)  all_32_0 = 0
% 6.81/1.74  | | | 
% 6.81/1.74  | | | REDUCE: (22), (29) imply:
% 6.81/1.74  | | |   (30)  $false
% 6.81/1.74  | | | 
% 6.81/1.74  | | | CLOSE: (30) is inconsistent.
% 6.81/1.74  | | | 
% 6.81/1.74  | | Case 2:
% 6.81/1.74  | | | 
% 6.81/1.74  | | |   (31)   ? [v0: any] :  ? [v1: any] : (in(all_32_1, all_18_2) = v1 &
% 6.81/1.74  | | |           in(all_32_1, all_18_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.81/1.74  | | | 
% 6.81/1.74  | | | DELTA: instantiating (31) with fresh symbols all_48_0, all_48_1 gives:
% 6.81/1.74  | | |   (32)  in(all_32_1, all_18_2) = all_48_0 & in(all_32_1, all_18_3) =
% 6.81/1.74  | | |         all_48_1 & ( ~ (all_48_0 = 0) |  ~ (all_48_1 = 0))
% 6.81/1.74  | | | 
% 6.81/1.74  | | | ALPHA: (32) implies:
% 6.81/1.74  | | |   (33)  in(all_32_1, all_18_3) = all_48_1
% 6.81/1.74  | | |   (34)  in(all_32_1, all_18_2) = all_48_0
% 6.81/1.74  | | |   (35)   ~ (all_48_0 = 0) |  ~ (all_48_1 = 0)
% 6.81/1.74  | | | 
% 6.81/1.74  | | | GROUND_INST: instantiating (5) with 0, all_48_1, all_18_3, all_32_1,
% 6.81/1.74  | | |              simplifying with (27), (33) gives:
% 6.81/1.74  | | |   (36)  all_48_1 = 0
% 6.81/1.74  | | | 
% 6.81/1.75  | | | GROUND_INST: instantiating (5) with 0, all_48_0, all_18_2, all_32_1,
% 6.81/1.75  | | |              simplifying with (26), (34) gives:
% 6.81/1.75  | | |   (37)  all_48_0 = 0
% 6.81/1.75  | | | 
% 6.81/1.75  | | | BETA: splitting (35) gives:
% 6.81/1.75  | | | 
% 6.81/1.75  | | | Case 1:
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | |   (38)   ~ (all_48_0 = 0)
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | | REDUCE: (37), (38) imply:
% 6.81/1.75  | | | |   (39)  $false
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | | CLOSE: (39) is inconsistent.
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | Case 2:
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | |   (40)   ~ (all_48_1 = 0)
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | | REDUCE: (36), (40) imply:
% 6.81/1.75  | | | |   (41)  $false
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | | CLOSE: (41) is inconsistent.
% 6.81/1.75  | | | | 
% 6.81/1.75  | | | End of split
% 6.81/1.75  | | | 
% 6.81/1.75  | | End of split
% 6.81/1.75  | | 
% 6.81/1.75  | End of split
% 6.81/1.75  | 
% 6.81/1.75  End of proof
% 6.81/1.75  % SZS output end Proof for theBenchmark
% 6.81/1.75  
% 6.81/1.75  1146ms
%------------------------------------------------------------------------------