TSTP Solution File: SEU159+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU159+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 : n019.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 17:42:53 EDT 2023

% Result   : Theorem 5.57s 1.53s
% Output   : Proof 6.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 13:06:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61  
% 0.21/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61  (2023-06-19)
% 0.21/0.61  
% 0.21/0.61  (c) Philipp Rümmer, 2009-2023
% 0.21/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61                Amanda Stjerna.
% 0.21/0.61  Free software under BSD-3-Clause.
% 0.21/0.61  
% 0.21/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61  
% 0.21/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62  Running up to 7 provers in parallel.
% 0.21/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.21/1.01  Prover 1: Preprocessing ...
% 2.21/1.01  Prover 4: Preprocessing ...
% 2.21/1.06  Prover 3: Preprocessing ...
% 2.21/1.06  Prover 0: Preprocessing ...
% 2.21/1.06  Prover 2: Preprocessing ...
% 2.21/1.06  Prover 6: Preprocessing ...
% 2.21/1.06  Prover 5: Preprocessing ...
% 3.79/1.23  Prover 5: Proving ...
% 3.79/1.23  Prover 6: Proving ...
% 3.80/1.24  Prover 1: Warning: ignoring some quantifiers
% 3.80/1.24  Prover 3: Warning: ignoring some quantifiers
% 3.80/1.24  Prover 4: Warning: ignoring some quantifiers
% 3.80/1.25  Prover 3: Constructing countermodel ...
% 3.80/1.25  Prover 1: Constructing countermodel ...
% 3.80/1.25  Prover 4: Constructing countermodel ...
% 3.80/1.25  Prover 0: Proving ...
% 3.80/1.26  Prover 2: Proving ...
% 4.83/1.45  Prover 1: gave up
% 4.83/1.45  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.83/1.47  Prover 3: gave up
% 4.83/1.49  Prover 7: Preprocessing ...
% 4.83/1.49  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.57/1.50  Prover 8: Preprocessing ...
% 5.57/1.52  Prover 7: Warning: ignoring some quantifiers
% 5.57/1.53  Prover 0: proved (904ms)
% 5.57/1.53  
% 5.57/1.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/1.53  
% 5.57/1.54  Prover 2: stopped
% 5.57/1.54  Prover 5: stopped
% 5.57/1.54  Prover 7: Constructing countermodel ...
% 5.57/1.54  Prover 6: stopped
% 5.57/1.54  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.57/1.54  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.57/1.54  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.57/1.55  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.57/1.56  Prover 13: Preprocessing ...
% 5.57/1.56  Prover 16: Preprocessing ...
% 5.57/1.56  Prover 10: Preprocessing ...
% 5.57/1.58  Prover 8: Warning: ignoring some quantifiers
% 5.57/1.58  Prover 11: Preprocessing ...
% 5.57/1.59  Prover 8: Constructing countermodel ...
% 6.36/1.60  Prover 13: Warning: ignoring some quantifiers
% 6.36/1.61  Prover 16: Warning: ignoring some quantifiers
% 6.36/1.61  Prover 4: Found proof (size 51)
% 6.36/1.61  Prover 4: proved (979ms)
% 6.36/1.61  Prover 10: Warning: ignoring some quantifiers
% 6.36/1.61  Prover 16: Constructing countermodel ...
% 6.36/1.61  Prover 13: Constructing countermodel ...
% 6.36/1.62  Prover 16: stopped
% 6.36/1.62  Prover 13: stopped
% 6.36/1.62  Prover 7: stopped
% 6.36/1.62  Prover 8: stopped
% 6.36/1.62  Prover 10: Constructing countermodel ...
% 6.36/1.62  Prover 10: stopped
% 6.36/1.64  Prover 11: Warning: ignoring some quantifiers
% 6.36/1.64  Prover 11: Constructing countermodel ...
% 6.36/1.65  Prover 11: stopped
% 6.36/1.65  
% 6.36/1.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/1.65  
% 6.36/1.66  % SZS output start Proof for theBenchmark
% 6.36/1.66  Assumptions after simplification:
% 6.36/1.66  ---------------------------------
% 6.36/1.66  
% 6.36/1.66    (commutativity_k2_tarski)
% 6.36/1.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | 
% 6.36/1.69      ~ $i(v1) |  ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) &  ! [v0: $i]
% 6.36/1.69    :  ! [v1: $i] :  ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ $i(v1) | 
% 6.36/1.69      ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.36/1.69  
% 6.36/1.69    (d2_tarski)
% 6.36/1.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v1 | v3 = v0 | 
% 6.36/1.69      ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ~ $i(v3) |  ~
% 6.36/1.69      $i(v2) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 6.36/1.69    ! [v3: int] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v1, v2) =
% 6.36/1.69        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 6.36/1.70    [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~
% 6.36/1.70      (in(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)) &  ? [v0: $i] :  !
% 6.36/1.70    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~ (unordered_pair(v1, v2) =
% 6.36/1.70        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: $i] :  ? [v5: any] :
% 6.36/1.70      (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) &  ~ (v4 = v1))) &
% 6.36/1.70        (v5 = 0 | v4 = v2 | v4 = v1)))
% 6.36/1.70  
% 6.36/1.70    (d3_tarski)
% 6.87/1.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.87/1.70      (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.87/1.70      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0: $i] :  !
% 6.87/1.70    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ~ $i(v1) |  ~
% 6.87/1.70      $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.87/1.70        in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 6.87/1.70      (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 6.87/1.70      $i(v0) | in(v2, v1) = 0)
% 6.87/1.70  
% 6.87/1.70    (t38_zfmisc_1)
% 6.87/1.70     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: any] :  ? [v5:
% 6.87/1.70      any] :  ? [v6: any] : (subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 &
% 6.87/1.70      in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6
% 6.87/1.70          = 0 & v5 = 0 &  ~ (v4 = 0)) | (v4 = 0 & ( ~ (v6 = 0) |  ~ (v5 = 0)))))
% 6.87/1.70  
% 6.87/1.70    (function-axioms)
% 6.87/1.71     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 6.87/1.71    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 6.87/1.71    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.87/1.71      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 6.87/1.71      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 6.87/1.71    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.87/1.71  
% 6.87/1.71  Further assumptions not needed in the proof:
% 6.87/1.71  --------------------------------------------
% 6.87/1.71  antisymmetry_r2_hidden, dt_k2_tarski, reflexivity_r1_tarski
% 6.87/1.71  
% 6.87/1.71  Those formulas are unsatisfiable:
% 6.87/1.71  ---------------------------------
% 6.87/1.71  
% 6.87/1.71  Begin of proof
% 6.87/1.71  | 
% 6.87/1.71  | ALPHA: (commutativity_k2_tarski) implies:
% 6.87/1.71  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 6.87/1.71  |            v2) |  ~ $i(v1) |  ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 6.87/1.71  |            $i(v2)))
% 6.87/1.71  | 
% 6.87/1.71  | ALPHA: (d2_tarski) implies:
% 6.87/1.71  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.87/1.71  |          (unordered_pair(v0, v1) = v2) |  ~ (in(v0, v2) = v3) |  ~ $i(v2) |  ~
% 6.87/1.71  |          $i(v1) |  ~ $i(v0))
% 6.87/1.71  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.87/1.71  |          (unordered_pair(v0, v1) = v2) |  ~ (in(v1, v2) = v3) |  ~ $i(v2) |  ~
% 6.87/1.71  |          $i(v1) |  ~ $i(v0))
% 6.87/1.72  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v1 | v3 =
% 6.87/1.72  |          v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ~
% 6.87/1.72  |          $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0))
% 6.87/1.72  | 
% 6.87/1.72  | ALPHA: (d3_tarski) implies:
% 6.87/1.72  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 6.87/1.72  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 6.87/1.72  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.87/1.72  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 6.87/1.72  |          (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |
% 6.87/1.72  |           ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 6.87/1.72  | 
% 6.87/1.72  | ALPHA: (function-axioms) implies:
% 6.87/1.72  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.87/1.72  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.87/1.72  | 
% 6.87/1.72  | DELTA: instantiating (t38_zfmisc_1) with fresh symbols all_10_0, all_10_1,
% 6.87/1.72  |        all_10_2, all_10_3, all_10_4, all_10_5, all_10_6 gives:
% 6.87/1.72  |   (8)  subset(all_10_3, all_10_4) = all_10_2 & unordered_pair(all_10_6,
% 6.87/1.72  |          all_10_5) = all_10_3 & in(all_10_5, all_10_4) = all_10_0 &
% 6.87/1.72  |        in(all_10_6, all_10_4) = all_10_1 & $i(all_10_3) & $i(all_10_4) &
% 6.87/1.72  |        $i(all_10_5) & $i(all_10_6) & ((all_10_0 = 0 & all_10_1 = 0 &  ~
% 6.87/1.72  |            (all_10_2 = 0)) | (all_10_2 = 0 & ( ~ (all_10_0 = 0) |  ~ (all_10_1
% 6.87/1.72  |                = 0))))
% 6.87/1.72  | 
% 6.87/1.72  | ALPHA: (8) implies:
% 6.87/1.72  |   (9)  $i(all_10_6)
% 6.87/1.72  |   (10)  $i(all_10_5)
% 6.87/1.72  |   (11)  $i(all_10_4)
% 6.87/1.72  |   (12)  in(all_10_6, all_10_4) = all_10_1
% 6.87/1.72  |   (13)  in(all_10_5, all_10_4) = all_10_0
% 6.87/1.72  |   (14)  unordered_pair(all_10_6, all_10_5) = all_10_3
% 6.87/1.72  |   (15)  subset(all_10_3, all_10_4) = all_10_2
% 6.87/1.72  |   (16)  (all_10_0 = 0 & all_10_1 = 0 &  ~ (all_10_2 = 0)) | (all_10_2 = 0 & (
% 6.87/1.72  |             ~ (all_10_0 = 0) |  ~ (all_10_1 = 0)))
% 6.87/1.72  | 
% 6.87/1.73  | GROUND_INST: instantiating (1) with all_10_5, all_10_6, all_10_3, simplifying
% 6.87/1.73  |              with (9), (10), (14) gives:
% 6.87/1.73  |   (17)  unordered_pair(all_10_5, all_10_6) = all_10_3 & $i(all_10_3)
% 6.87/1.73  | 
% 6.87/1.73  | ALPHA: (17) implies:
% 6.87/1.73  |   (18)  $i(all_10_3)
% 6.87/1.73  | 
% 6.87/1.73  | GROUND_INST: instantiating (5) with all_10_3, all_10_4, all_10_2, simplifying
% 6.87/1.73  |              with (11), (15), (18) gives:
% 6.87/1.73  |   (19)  all_10_2 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.87/1.73  |             all_10_3) = 0 & in(v0, all_10_4) = v1 & $i(v0))
% 6.87/1.73  | 
% 6.87/1.73  | BETA: splitting (16) gives:
% 6.87/1.73  | 
% 6.87/1.73  | Case 1:
% 6.87/1.73  | | 
% 6.87/1.73  | |   (20)  all_10_0 = 0 & all_10_1 = 0 &  ~ (all_10_2 = 0)
% 6.87/1.73  | | 
% 6.87/1.73  | | ALPHA: (20) implies:
% 6.87/1.73  | |   (21)  all_10_1 = 0
% 6.87/1.73  | |   (22)  all_10_0 = 0
% 6.87/1.73  | |   (23)   ~ (all_10_2 = 0)
% 6.87/1.73  | | 
% 6.87/1.73  | | REDUCE: (13), (22) imply:
% 6.87/1.73  | |   (24)  in(all_10_5, all_10_4) = 0
% 6.87/1.73  | | 
% 6.87/1.73  | | REDUCE: (12), (21) imply:
% 6.87/1.73  | |   (25)  in(all_10_6, all_10_4) = 0
% 6.87/1.73  | | 
% 6.87/1.73  | | BETA: splitting (19) gives:
% 6.87/1.73  | | 
% 6.87/1.73  | | Case 1:
% 6.87/1.73  | | | 
% 6.87/1.73  | | |   (26)  all_10_2 = 0
% 6.87/1.73  | | | 
% 6.87/1.73  | | | REDUCE: (23), (26) imply:
% 6.87/1.73  | | |   (27)  $false
% 6.87/1.73  | | | 
% 6.87/1.73  | | | CLOSE: (27) is inconsistent.
% 6.87/1.73  | | | 
% 6.87/1.73  | | Case 2:
% 6.87/1.73  | | | 
% 6.87/1.73  | | |   (28)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_10_3) = 0 &
% 6.87/1.73  | | |           in(v0, all_10_4) = v1 & $i(v0))
% 6.87/1.73  | | | 
% 6.87/1.73  | | | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1 gives:
% 6.87/1.73  | | |   (29)   ~ (all_29_0 = 0) & in(all_29_1, all_10_3) = 0 & in(all_29_1,
% 6.87/1.73  | | |           all_10_4) = all_29_0 & $i(all_29_1)
% 6.87/1.73  | | | 
% 6.87/1.73  | | | ALPHA: (29) implies:
% 6.87/1.73  | | |   (30)   ~ (all_29_0 = 0)
% 6.87/1.73  | | |   (31)  $i(all_29_1)
% 6.87/1.73  | | |   (32)  in(all_29_1, all_10_4) = all_29_0
% 6.87/1.73  | | |   (33)  in(all_29_1, all_10_3) = 0
% 6.87/1.73  | | | 
% 6.87/1.74  | | | GROUND_INST: instantiating (4) with all_10_6, all_10_5, all_10_3,
% 6.87/1.74  | | |              all_29_1, simplifying with (9), (10), (14), (18), (31), (33)
% 6.87/1.74  | | |              gives:
% 6.87/1.74  | | |   (34)  all_29_1 = all_10_5 | all_29_1 = all_10_6
% 6.87/1.74  | | | 
% 6.87/1.74  | | | BETA: splitting (34) gives:
% 6.87/1.74  | | | 
% 6.87/1.74  | | | Case 1:
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | |   (35)  all_29_1 = all_10_5
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | REDUCE: (32), (35) imply:
% 6.87/1.74  | | | |   (36)  in(all_10_5, all_10_4) = all_29_0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_5,
% 6.87/1.74  | | | |              simplifying with (24), (36) gives:
% 6.87/1.74  | | | |   (37)  all_29_0 = 0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | REDUCE: (30), (37) imply:
% 6.87/1.74  | | | |   (38)  $false
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | CLOSE: (38) is inconsistent.
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | Case 2:
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | |   (39)  all_29_1 = all_10_6
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | REDUCE: (32), (39) imply:
% 6.87/1.74  | | | |   (40)  in(all_10_6, all_10_4) = all_29_0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_6,
% 6.87/1.74  | | | |              simplifying with (25), (40) gives:
% 6.87/1.74  | | | |   (41)  all_29_0 = 0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | REDUCE: (30), (41) imply:
% 6.87/1.74  | | | |   (42)  $false
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | CLOSE: (42) is inconsistent.
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | End of split
% 6.87/1.74  | | | 
% 6.87/1.74  | | End of split
% 6.87/1.74  | | 
% 6.87/1.74  | Case 2:
% 6.87/1.74  | | 
% 6.87/1.74  | |   (43)  all_10_2 = 0 & ( ~ (all_10_0 = 0) |  ~ (all_10_1 = 0))
% 6.87/1.74  | | 
% 6.87/1.74  | | ALPHA: (43) implies:
% 6.87/1.74  | |   (44)  all_10_2 = 0
% 6.87/1.74  | |   (45)   ~ (all_10_0 = 0) |  ~ (all_10_1 = 0)
% 6.87/1.74  | | 
% 6.87/1.74  | | REDUCE: (15), (44) imply:
% 6.87/1.74  | |   (46)  subset(all_10_3, all_10_4) = 0
% 6.87/1.74  | | 
% 6.87/1.74  | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_5, all_10_0,
% 6.87/1.74  | |              simplifying with (10), (11), (13), (18), (46) gives:
% 6.87/1.74  | |   (47)  all_10_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3)
% 6.87/1.74  | |           = v0)
% 6.87/1.74  | | 
% 6.87/1.74  | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_6, all_10_1,
% 6.87/1.74  | |              simplifying with (9), (11), (12), (18), (46) gives:
% 6.87/1.74  | |   (48)  all_10_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3)
% 6.87/1.74  | |           = v0)
% 6.87/1.74  | | 
% 6.87/1.74  | | BETA: splitting (45) gives:
% 6.87/1.74  | | 
% 6.87/1.74  | | Case 1:
% 6.87/1.74  | | | 
% 6.87/1.74  | | |   (49)   ~ (all_10_0 = 0)
% 6.87/1.74  | | | 
% 6.87/1.74  | | | BETA: splitting (47) gives:
% 6.87/1.74  | | | 
% 6.87/1.74  | | | Case 1:
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | |   (50)  all_10_0 = 0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | REDUCE: (49), (50) imply:
% 6.87/1.74  | | | |   (51)  $false
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | CLOSE: (51) is inconsistent.
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | Case 2:
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | |   (52)   ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3) = v0)
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | DELTA: instantiating (52) with fresh symbol all_50_0 gives:
% 6.87/1.74  | | | |   (53)   ~ (all_50_0 = 0) & in(all_10_5, all_10_3) = all_50_0
% 6.87/1.74  | | | | 
% 6.87/1.74  | | | | ALPHA: (53) implies:
% 6.87/1.74  | | | |   (54)   ~ (all_50_0 = 0)
% 6.87/1.75  | | | |   (55)  in(all_10_5, all_10_3) = all_50_0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | GROUND_INST: instantiating (3) with all_10_6, all_10_5, all_10_3,
% 6.87/1.75  | | | |              all_50_0, simplifying with (9), (10), (14), (18), (55)
% 6.87/1.75  | | | |              gives:
% 6.87/1.75  | | | |   (56)  all_50_0 = 0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | REDUCE: (54), (56) imply:
% 6.87/1.75  | | | |   (57)  $false
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | CLOSE: (57) is inconsistent.
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | End of split
% 6.87/1.75  | | | 
% 6.87/1.75  | | Case 2:
% 6.87/1.75  | | | 
% 6.87/1.75  | | |   (58)   ~ (all_10_1 = 0)
% 6.87/1.75  | | | 
% 6.87/1.75  | | | BETA: splitting (48) gives:
% 6.87/1.75  | | | 
% 6.87/1.75  | | | Case 1:
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | |   (59)  all_10_1 = 0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | REDUCE: (58), (59) imply:
% 6.87/1.75  | | | |   (60)  $false
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | CLOSE: (60) is inconsistent.
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | Case 2:
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | |   (61)   ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3) = v0)
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | DELTA: instantiating (61) with fresh symbol all_50_0 gives:
% 6.87/1.75  | | | |   (62)   ~ (all_50_0 = 0) & in(all_10_6, all_10_3) = all_50_0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | ALPHA: (62) implies:
% 6.87/1.75  | | | |   (63)   ~ (all_50_0 = 0)
% 6.87/1.75  | | | |   (64)  in(all_10_6, all_10_3) = all_50_0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | GROUND_INST: instantiating (2) with all_10_6, all_10_5, all_10_3,
% 6.87/1.75  | | | |              all_50_0, simplifying with (9), (10), (14), (18), (64)
% 6.87/1.75  | | | |              gives:
% 6.87/1.75  | | | |   (65)  all_50_0 = 0
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | REDUCE: (63), (65) imply:
% 6.87/1.75  | | | |   (66)  $false
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | | CLOSE: (66) is inconsistent.
% 6.87/1.75  | | | | 
% 6.87/1.75  | | | End of split
% 6.87/1.75  | | | 
% 6.87/1.75  | | End of split
% 6.87/1.75  | | 
% 6.87/1.75  | End of split
% 6.87/1.75  | 
% 6.87/1.75  End of proof
% 6.87/1.75  % SZS output end Proof for theBenchmark
% 6.87/1.75  
% 6.87/1.75  1140ms
%------------------------------------------------------------------------------