TSTP Solution File: KRS070+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS070+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n028.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 05:51:08 EDT 2023

% Result   : Unsatisfiable 6.49s 1.93s
% Output   : Proof 9.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KRS070+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon Aug 28 01:46:54 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.63  ________       _____
% 0.22/0.63  ___  __ \_________(_)________________________________
% 0.22/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63  
% 0.22/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63  (2023-06-19)
% 0.22/0.63  
% 0.22/0.63  (c) Philipp Rümmer, 2009-2023
% 0.22/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63                Amanda Stjerna.
% 0.22/0.63  Free software under BSD-3-Clause.
% 0.22/0.63  
% 0.22/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63  
% 0.22/0.64  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.65  Running up to 7 provers in parallel.
% 0.22/0.68  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.68  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.68  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.68  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.68  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.68  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.68  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.19  Prover 1: Preprocessing ...
% 2.49/1.19  Prover 4: Preprocessing ...
% 2.92/1.24  Prover 5: Preprocessing ...
% 2.92/1.24  Prover 2: Preprocessing ...
% 2.92/1.24  Prover 6: Preprocessing ...
% 2.92/1.24  Prover 0: Preprocessing ...
% 2.92/1.24  Prover 3: Preprocessing ...
% 5.21/1.72  Prover 5: Proving ...
% 5.21/1.73  Prover 2: Proving ...
% 6.03/1.88  Prover 1: Constructing countermodel ...
% 6.03/1.90  Prover 6: Proving ...
% 6.49/1.92  Prover 3: Constructing countermodel ...
% 6.49/1.93  Prover 5: proved (1260ms)
% 6.49/1.93  
% 6.49/1.93  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.49/1.93  
% 6.49/1.93  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.49/1.94  Prover 2: stopped
% 6.49/1.94  Prover 3: stopped
% 6.49/1.94  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.49/1.94  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.49/1.96  Prover 6: stopped
% 6.49/1.97  Prover 4: Constructing countermodel ...
% 6.49/1.98  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.84/2.05  Prover 10: Preprocessing ...
% 6.84/2.07  Prover 0: Proving ...
% 6.84/2.07  Prover 0: stopped
% 6.84/2.09  Prover 8: Preprocessing ...
% 6.84/2.09  Prover 7: Preprocessing ...
% 6.84/2.10  Prover 11: Preprocessing ...
% 6.84/2.12  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.84/2.17  Prover 1: gave up
% 6.84/2.18  Prover 13: Preprocessing ...
% 7.62/2.20  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.97/2.22  Prover 10: Warning: ignoring some quantifiers
% 7.97/2.22  Prover 10: Constructing countermodel ...
% 7.97/2.24  Prover 7: Warning: ignoring some quantifiers
% 8.15/2.27  Prover 7: Constructing countermodel ...
% 8.15/2.29  Prover 13: Warning: ignoring some quantifiers
% 8.15/2.31  Prover 13: Constructing countermodel ...
% 8.15/2.31  Prover 16: Preprocessing ...
% 8.63/2.35  Prover 10: Found proof (size 15)
% 8.63/2.35  Prover 4: Found proof (size 31)
% 8.63/2.35  Prover 4: proved (1678ms)
% 8.63/2.35  Prover 10: proved (404ms)
% 8.63/2.35  Prover 7: stopped
% 8.63/2.36  Prover 13: stopped
% 8.91/2.39  Prover 16: Warning: ignoring some quantifiers
% 8.91/2.39  Prover 16: Constructing countermodel ...
% 8.91/2.39  Prover 16: stopped
% 8.91/2.40  Prover 8: Warning: ignoring some quantifiers
% 8.91/2.43  Prover 8: Constructing countermodel ...
% 8.91/2.44  Prover 8: stopped
% 9.24/2.45  Prover 11: Constructing countermodel ...
% 9.24/2.46  Prover 11: stopped
% 9.24/2.46  
% 9.24/2.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/2.46  
% 9.32/2.47  % SZS output start Proof for theBenchmark
% 9.32/2.48  Assumptions after simplification:
% 9.32/2.48  ---------------------------------
% 9.32/2.48  
% 9.32/2.48    (axiom_16)
% 9.32/2.51     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rrx(v0, v1) = v2) | 
% 9.32/2.51      ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rrx4(v0, v1) = v3)) & 
% 9.32/2.51    ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx4(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 9.32/2.51      rrx(v0, v1) = 0)
% 9.32/2.51  
% 9.32/2.51    (axiom_2)
% 9.56/2.53     ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] :  ! [v3: $i] : (v1 = 0 |  ~
% 9.56/2.53      (rrx4(v0, v3) = 0) |  ~ (rrx3(v0, v2) = 0) |  ~ (cUnsatisfiable(v0) = v1) | 
% 9.56/2.53      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: $i] :  ? [v6: int]
% 9.56/2.53      :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ($i(v5) & ((v8 = 0 & v7 = 0 &
% 9.56/2.53            v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) = 0 & cc1(v5) = 0) | ( ~ (v9 = 0)
% 9.56/2.53            & cc2(v3) = v9) | ( ~ (v4 = 0) & cc1(v2) = v4)))) &  ! [v0: $i] :  !
% 9.56/2.53    [v1: int] :  ! [v2: $i] :  ! [v3: $i] : (v1 = 0 |  ~ (rrx4(v0, v3) = 0) |  ~
% 9.56/2.53      (cc1(v2) = 0) |  ~ (cUnsatisfiable(v0) = v1) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 9.56/2.53      $i(v0) |  ? [v4: int] :  ? [v5: $i] :  ? [v6: int] :  ? [v7: int] :  ? [v8:
% 9.56/2.53        int] :  ? [v9: int] : ($i(v5) & ((v8 = 0 & v7 = 0 & v6 = 0 & rrx3(v0, v5)
% 9.56/2.53            = 0 & cc2(v5) = 0 & cc1(v5) = 0) | ( ~ (v9 = 0) & cc2(v3) = v9) | ( ~
% 9.56/2.53            (v4 = 0) & rrx3(v0, v2) = v4)))) &  ! [v0: $i] :  ! [v1: int] :  !
% 9.56/2.53    [v2: $i] :  ! [v3: $i] : (v1 = 0 |  ~ (rrx3(v0, v2) = 0) |  ~ (cc2(v3) = 0) | 
% 9.56/2.53      ~ (cUnsatisfiable(v0) = v1) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ? [v4:
% 9.56/2.53        int] :  ? [v5: $i] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 9.56/2.53        int] : ($i(v5) & ((v8 = 0 & v7 = 0 & v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) =
% 9.56/2.53            0 & cc1(v5) = 0) | ( ~ (v9 = 0) & rrx4(v0, v3) = v9) | ( ~ (v4 = 0) &
% 9.56/2.53            cc1(v2) = v4)))) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] :  ! [v3:
% 9.56/2.53      $i] : (v1 = 0 |  ~ (cc2(v3) = 0) |  ~ (cc1(v2) = 0) |  ~ (cUnsatisfiable(v0)
% 9.56/2.53        = v1) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: $i] : 
% 9.56/2.53      ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ($i(v5) & ((v8 =
% 9.56/2.53            0 & v7 = 0 & v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) = 0 & cc1(v5) = 0) |
% 9.56/2.53          ( ~ (v9 = 0) & rrx4(v0, v3) = v9) | ( ~ (v4 = 0) & rrx3(v0, v2) = v4))))
% 9.56/2.53    &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) |  ~ (cUnsatisfiable(v0)
% 9.56/2.53        = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (cc2(v1) = v2
% 9.56/2.53        & cc1(v1) = v3 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i]
% 9.56/2.53    : ( ~ (cc2(v1) = 0) |  ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 9.56/2.53      [v2: any] :  ? [v3: any] : (rrx3(v0, v1) = v2 & cc1(v1) = v3 & ( ~ (v3 = 0)
% 9.56/2.53          |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cc1(v1) = 0) |  ~
% 9.56/2.53      (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 9.56/2.53        any] : (rrx3(v0, v1) = v2 & cc2(v1) = v3 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &
% 9.56/2.53     ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 9.56/2.53      (rrx4(v0, v1) = 0 & cc2(v1) = 0 & $i(v1))) &  ! [v0: $i] : ( ~
% 9.56/2.53      (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : (rrx3(v0, v1) = 0 &
% 9.56/2.53        cc1(v1) = 0 & $i(v1)))
% 9.56/2.53  
% 9.56/2.53    (axiom_3)
% 9.56/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (rrx(v0, v2) = 0) |  ~
% 9.56/2.53      (rrx(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0))
% 9.56/2.53  
% 9.56/2.53    (axiom_8)
% 9.56/2.53    cUnsatisfiable(i2003_11_14_17_18_32242) = 0 & $i(i2003_11_14_17_18_32242)
% 9.56/2.53  
% 9.56/2.53    (axiom_9)
% 9.56/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rrx(v0, v1) = v2) | 
% 9.56/2.53      ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rrx3(v0, v1) = v3)) & 
% 9.56/2.53    ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 9.56/2.53      rrx(v0, v1) = 0)
% 9.56/2.53  
% 9.56/2.53    (function-axioms)
% 9.56/2.54     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 9.56/2.54    [v3: $i] : (v1 = v0 |  ~ (rrxa(v3, v2) = v1) |  ~ (rrxa(v3, v2) = v0)) &  !
% 9.56/2.54    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 9.56/2.54      $i] : (v1 = v0 |  ~ (rrx4a(v3, v2) = v1) |  ~ (rrx4a(v3, v2) = v0)) &  !
% 9.56/2.54    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 9.56/2.54      $i] : (v1 = v0 |  ~ (rrx4(v3, v2) = v1) |  ~ (rrx4(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx3a(v3, v2) = v1) |  ~ (rrx3a(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx3(v3, v2) = v1) |  ~ (rrx3(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx2a(v3, v2) = v1) |  ~ (rrx2a(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx2(v3, v2) = v1) |  ~ (rrx2(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx1a(v3, v2) = v1) |  ~ (rrx1a(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx1(v3, v2) = v1) |  ~ (rrx1(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.56/2.54    : (v1 = v0 |  ~ (rrx(v3, v2) = v1) |  ~ (rrx(v3, v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.56/2.54      ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.56/2.54      ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.56/2.54      ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.56/2.54      ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0)) &  ! [v0:
% 9.56/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.56/2.54      ~ (cc2(v2) = v1) |  ~ (cc2(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.56/2.54      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (cc1(v2) = v1) |  ~
% 9.56/2.54      (cc1(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 9.56/2.54    ! [v2: $i] : (v1 = v0 |  ~ (cUnsatisfiable(v2) = v1) |  ~ (cUnsatisfiable(v2)
% 9.56/2.54        = v0))
% 9.56/2.54  
% 9.56/2.54  Further assumptions not needed in the proof:
% 9.56/2.54  --------------------------------------------
% 9.56/2.54  axiom_0, axiom_1, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15,
% 9.56/2.54  axiom_4, axiom_5, axiom_6, axiom_7, cUnsatisfiable_substitution_1,
% 9.56/2.54  cc1_substitution_1, cc2_substitution_1, cowlNothing_substitution_1,
% 9.56/2.54  cowlThing_substitution_1, rrx1_substitution_1, rrx1_substitution_2,
% 9.56/2.54  rrx1a_substitution_1, rrx1a_substitution_2, rrx2_substitution_1,
% 9.56/2.54  rrx2_substitution_2, rrx2a_substitution_1, rrx2a_substitution_2,
% 9.56/2.54  rrx3_substitution_1, rrx3_substitution_2, rrx3a_substitution_1,
% 9.56/2.54  rrx3a_substitution_2, rrx4_substitution_1, rrx4_substitution_2,
% 9.56/2.54  rrx4a_substitution_1, rrx4a_substitution_2, rrx_substitution_1,
% 9.56/2.54  rrx_substitution_2, rrxa_substitution_1, rrxa_substitution_2,
% 9.56/2.54  xsd_integer_substitution_1, xsd_string_substitution_1
% 9.56/2.54  
% 9.56/2.54  Those formulas are unsatisfiable:
% 9.56/2.54  ---------------------------------
% 9.56/2.54  
% 9.56/2.54  Begin of proof
% 9.56/2.54  | 
% 9.56/2.54  | ALPHA: (axiom_2) implies:
% 9.56/2.54  |   (1)   ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 9.56/2.54  |          (rrx3(v0, v1) = 0 & cc1(v1) = 0 & $i(v1)))
% 9.56/2.54  |   (2)   ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 9.56/2.54  |          (rrx4(v0, v1) = 0 & cc2(v1) = 0 & $i(v1)))
% 9.70/2.55  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cc1(v1) = 0) |  ~ (cUnsatisfiable(v0)
% 9.70/2.55  |            = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] :
% 9.70/2.55  |          (rrx3(v0, v1) = v2 & cc2(v1) = v3 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 9.70/2.55  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) |  ~
% 9.70/2.55  |          (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ?
% 9.70/2.55  |          [v3: any] : (cc2(v1) = v2 & cc1(v1) = v3 & ( ~ (v3 = 0) |  ~ (v2 =
% 9.70/2.55  |                0))))
% 9.70/2.55  | 
% 9.70/2.55  | ALPHA: (axiom_8) implies:
% 9.70/2.55  |   (5)  $i(i2003_11_14_17_18_32242)
% 9.70/2.55  |   (6)  cUnsatisfiable(i2003_11_14_17_18_32242) = 0
% 9.70/2.55  | 
% 9.70/2.55  | ALPHA: (axiom_9) implies:
% 9.70/2.55  |   (7)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) |  ~ $i(v1) |  ~
% 9.70/2.55  |          $i(v0) | rrx(v0, v1) = 0)
% 9.70/2.55  | 
% 9.70/2.55  | ALPHA: (axiom_16) implies:
% 9.70/2.55  |   (8)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rrx4(v0, v1) = 0) |  ~ $i(v1) |  ~
% 9.70/2.55  |          $i(v0) | rrx(v0, v1) = 0)
% 9.70/2.55  | 
% 9.70/2.55  | ALPHA: (function-axioms) implies:
% 9.70/2.55  |   (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.70/2.55  |        (v1 = v0 |  ~ (cc2(v2) = v1) |  ~ (cc2(v2) = v0))
% 9.70/2.55  |   (10)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 9.70/2.55  |         :  ! [v3: $i] : (v1 = v0 |  ~ (rrx3(v3, v2) = v1) |  ~ (rrx3(v3, v2) =
% 9.70/2.55  |             v0))
% 9.70/2.55  | 
% 9.70/2.55  | GROUND_INST: instantiating (2) with i2003_11_14_17_18_32242, simplifying with
% 9.70/2.55  |              (5), (6) gives:
% 9.70/2.55  |   (11)   ? [v0: $i] : (rrx4(i2003_11_14_17_18_32242, v0) = 0 & cc2(v0) = 0 &
% 9.70/2.55  |           $i(v0))
% 9.70/2.55  | 
% 9.70/2.55  | GROUND_INST: instantiating (1) with i2003_11_14_17_18_32242, simplifying with
% 9.70/2.55  |              (5), (6) gives:
% 9.70/2.55  |   (12)   ? [v0: $i] : (rrx3(i2003_11_14_17_18_32242, v0) = 0 & cc1(v0) = 0 &
% 9.70/2.55  |           $i(v0))
% 9.70/2.55  | 
% 9.70/2.55  | DELTA: instantiating (12) with fresh symbol all_25_0 gives:
% 9.70/2.55  |   (13)  rrx3(i2003_11_14_17_18_32242, all_25_0) = 0 & cc1(all_25_0) = 0 &
% 9.70/2.55  |         $i(all_25_0)
% 9.70/2.55  | 
% 9.70/2.55  | ALPHA: (13) implies:
% 9.70/2.56  |   (14)  $i(all_25_0)
% 9.70/2.56  |   (15)  cc1(all_25_0) = 0
% 9.70/2.56  |   (16)  rrx3(i2003_11_14_17_18_32242, all_25_0) = 0
% 9.70/2.56  | 
% 9.70/2.56  | DELTA: instantiating (11) with fresh symbol all_27_0 gives:
% 9.70/2.56  |   (17)  rrx4(i2003_11_14_17_18_32242, all_27_0) = 0 & cc2(all_27_0) = 0 &
% 9.70/2.56  |         $i(all_27_0)
% 9.70/2.56  | 
% 9.70/2.56  | ALPHA: (17) implies:
% 9.70/2.56  |   (18)  $i(all_27_0)
% 9.70/2.56  |   (19)  cc2(all_27_0) = 0
% 9.70/2.56  |   (20)  rrx4(i2003_11_14_17_18_32242, all_27_0) = 0
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (3) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56  |              simplifying with (5), (6), (14), (15) gives:
% 9.70/2.56  |   (21)   ? [v0: any] :  ? [v1: any] : (rrx3(i2003_11_14_17_18_32242, all_25_0)
% 9.70/2.56  |           = v0 & cc2(all_25_0) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (4) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56  |              simplifying with (5), (6), (14), (16) gives:
% 9.70/2.56  |   (22)   ? [v0: any] :  ? [v1: any] : (cc2(all_25_0) = v0 & cc1(all_25_0) = v1
% 9.70/2.56  |           & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (7) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56  |              simplifying with (5), (14), (16) gives:
% 9.70/2.56  |   (23)  rrx(i2003_11_14_17_18_32242, all_25_0) = 0
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (8) with i2003_11_14_17_18_32242, all_27_0,
% 9.70/2.56  |              simplifying with (5), (18), (20) gives:
% 9.70/2.56  |   (24)  rrx(i2003_11_14_17_18_32242, all_27_0) = 0
% 9.70/2.56  | 
% 9.70/2.56  | DELTA: instantiating (22) with fresh symbols all_35_0, all_35_1 gives:
% 9.70/2.56  |   (25)  cc2(all_25_0) = all_35_1 & cc1(all_25_0) = all_35_0 & ( ~ (all_35_0 =
% 9.70/2.56  |             0) |  ~ (all_35_1 = 0))
% 9.70/2.56  | 
% 9.70/2.56  | ALPHA: (25) implies:
% 9.70/2.56  |   (26)  cc2(all_25_0) = all_35_1
% 9.70/2.56  | 
% 9.70/2.56  | DELTA: instantiating (21) with fresh symbols all_39_0, all_39_1 gives:
% 9.70/2.56  |   (27)  rrx3(i2003_11_14_17_18_32242, all_25_0) = all_39_1 & cc2(all_25_0) =
% 9.70/2.56  |         all_39_0 & ( ~ (all_39_0 = 0) |  ~ (all_39_1 = 0))
% 9.70/2.56  | 
% 9.70/2.56  | ALPHA: (27) implies:
% 9.70/2.56  |   (28)  cc2(all_25_0) = all_39_0
% 9.70/2.56  |   (29)  rrx3(i2003_11_14_17_18_32242, all_25_0) = all_39_1
% 9.70/2.56  |   (30)   ~ (all_39_0 = 0) |  ~ (all_39_1 = 0)
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (9) with all_35_1, all_39_0, all_25_0, simplifying
% 9.70/2.56  |              with (26), (28) gives:
% 9.70/2.56  |   (31)  all_39_0 = all_35_1
% 9.70/2.56  | 
% 9.70/2.56  | GROUND_INST: instantiating (10) with 0, all_39_1, all_25_0,
% 9.70/2.56  |              i2003_11_14_17_18_32242, simplifying with (16), (29) gives:
% 9.70/2.56  |   (32)  all_39_1 = 0
% 9.70/2.56  | 
% 9.70/2.56  | BETA: splitting (30) gives:
% 9.70/2.56  | 
% 9.70/2.57  | Case 1:
% 9.70/2.57  | | 
% 9.70/2.57  | |   (33)   ~ (all_39_0 = 0)
% 9.70/2.57  | | 
% 9.70/2.57  | | REDUCE: (31), (33) imply:
% 9.70/2.57  | |   (34)   ~ (all_35_1 = 0)
% 9.70/2.57  | | 
% 9.70/2.57  | | GROUND_INST: instantiating (axiom_3) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.57  | |              all_27_0, simplifying with (5), (14), (18), (23), (24) gives:
% 9.70/2.57  | |   (35)  all_27_0 = all_25_0
% 9.70/2.57  | | 
% 9.70/2.57  | | REDUCE: (19), (35) imply:
% 9.70/2.57  | |   (36)  cc2(all_25_0) = 0
% 9.70/2.57  | | 
% 9.70/2.57  | | GROUND_INST: instantiating (9) with all_35_1, 0, all_25_0, simplifying with
% 9.70/2.57  | |              (26), (36) gives:
% 9.70/2.57  | |   (37)  all_35_1 = 0
% 9.70/2.57  | | 
% 9.70/2.57  | | REDUCE: (34), (37) imply:
% 9.70/2.57  | |   (38)  $false
% 9.70/2.57  | | 
% 9.70/2.57  | | CLOSE: (38) is inconsistent.
% 9.70/2.57  | | 
% 9.70/2.57  | Case 2:
% 9.70/2.57  | | 
% 9.70/2.57  | |   (39)   ~ (all_39_1 = 0)
% 9.70/2.57  | | 
% 9.70/2.57  | | REDUCE: (32), (39) imply:
% 9.70/2.57  | |   (40)  $false
% 9.70/2.57  | | 
% 9.70/2.57  | | CLOSE: (40) is inconsistent.
% 9.70/2.57  | | 
% 9.70/2.57  | End of split
% 9.70/2.57  | 
% 9.70/2.57  End of proof
% 9.70/2.57  % SZS output end Proof for theBenchmark
% 9.70/2.57  
% 9.70/2.57  1934ms
%------------------------------------------------------------------------------