TSTP Solution File: KRS170+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS170+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 : n026.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 05:51:31 EDT 2023

% Result   : Theorem 4.39s 1.31s
% Output   : Proof 6.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS170+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 02:15:19 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.61  ________       _____
% 0.19/0.61  ___  __ \_________(_)________________________________
% 0.19/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61  
% 0.19/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61  (2023-06-19)
% 0.19/0.61  
% 0.19/0.61  (c) Philipp Rümmer, 2009-2023
% 0.19/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61                Amanda Stjerna.
% 0.19/0.61  Free software under BSD-3-Clause.
% 0.19/0.61  
% 0.19/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61  
% 0.19/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.73/0.97  Prover 1: Preprocessing ...
% 1.73/0.97  Prover 4: Preprocessing ...
% 2.30/1.02  Prover 6: Preprocessing ...
% 2.30/1.02  Prover 3: Preprocessing ...
% 2.30/1.02  Prover 2: Preprocessing ...
% 2.30/1.02  Prover 5: Preprocessing ...
% 2.30/1.02  Prover 0: Preprocessing ...
% 2.80/1.13  Prover 2: Proving ...
% 2.80/1.13  Prover 5: Proving ...
% 2.80/1.15  Prover 1: Constructing countermodel ...
% 2.80/1.16  Prover 6: Constructing countermodel ...
% 2.80/1.17  Prover 3: Constructing countermodel ...
% 3.47/1.18  Prover 4: Constructing countermodel ...
% 3.55/1.20  Prover 0: Proving ...
% 4.39/1.31  Prover 3: proved (674ms)
% 4.39/1.31  
% 4.39/1.31  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/1.31  
% 4.39/1.31  Prover 6: stopped
% 4.39/1.31  Prover 0: stopped
% 4.39/1.32  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.39/1.32  Prover 2: stopped
% 4.39/1.32  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.39/1.32  Prover 5: stopped
% 4.39/1.32  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.39/1.32  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.39/1.32  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.39/1.34  Prover 13: Preprocessing ...
% 4.39/1.34  Prover 10: Preprocessing ...
% 4.39/1.34  Prover 11: Preprocessing ...
% 4.39/1.35  Prover 7: Preprocessing ...
% 4.39/1.35  Prover 8: Preprocessing ...
% 4.39/1.36  Prover 10: Warning: ignoring some quantifiers
% 4.39/1.37  Prover 10: Constructing countermodel ...
% 4.39/1.37  Prover 7: Warning: ignoring some quantifiers
% 4.39/1.37  Prover 7: Constructing countermodel ...
% 4.39/1.37  Prover 13: Warning: ignoring some quantifiers
% 4.39/1.38  Prover 13: Constructing countermodel ...
% 4.97/1.41  Prover 10: gave up
% 4.97/1.41  Prover 8: Warning: ignoring some quantifiers
% 4.97/1.41  Prover 13: gave up
% 4.97/1.42  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.97/1.42  Prover 8: Constructing countermodel ...
% 4.97/1.42  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.97/1.42  Prover 7: gave up
% 4.97/1.44  Prover 16: Preprocessing ...
% 4.97/1.44  Prover 1: Found proof (size 53)
% 4.97/1.44  Prover 1: proved (814ms)
% 4.97/1.44  Prover 4: stopped
% 4.97/1.44  Prover 8: stopped
% 4.97/1.44  Prover 19: Preprocessing ...
% 4.97/1.45  Prover 11: Constructing countermodel ...
% 4.97/1.46  Prover 11: stopped
% 4.97/1.46  Prover 16: Warning: ignoring some quantifiers
% 4.97/1.46  Prover 16: Constructing countermodel ...
% 4.97/1.47  Prover 16: stopped
% 4.97/1.49  Prover 19: Warning: ignoring some quantifiers
% 4.97/1.50  Prover 19: Constructing countermodel ...
% 4.97/1.50  Prover 19: stopped
% 4.97/1.50  
% 4.97/1.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.97/1.50  
% 4.97/1.51  % SZS output start Proof for theBenchmark
% 4.97/1.51  Assumptions after simplification:
% 4.97/1.51  ---------------------------------
% 4.97/1.51  
% 4.97/1.51    (axiom_0)
% 4.97/1.55     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~ $i(v0)) & 
% 4.97/1.55    ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 4.97/1.55  
% 4.97/1.55    (axiom_1)
% 4.97/1.55     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_string(v0) = v1) |  ~ $i(v0) |
% 4.97/1.55      xsd_integer(v0) = 0) &  ! [v0: $i] : ( ~ (xsd_string(v0) = 0) |  ~ $i(v0) | 
% 4.97/1.55      ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 4.97/1.55  
% 4.97/1.55    (axiom_2)
% 4.97/1.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasLeader(v0, v1) =
% 4.97/1.55        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rhasHead(v0,
% 4.97/1.55          v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) | 
% 4.97/1.55      ~ $i(v1) |  ~ $i(v0) | rhasHead(v0, v1) = 0)
% 4.97/1.55  
% 4.97/1.55    (the_axiom)
% 4.97/1.56     ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) & rhasLeader(v0, v1) =
% 4.97/1.56      v2 & rhasHead(v0, v1) = 0 & $i(v1) & $i(v0)) |  ? [v0: $i] :  ? [v1: $i] : 
% 4.97/1.56    ? [v2: int] : ( ~ (v2 = 0) & rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 &
% 4.97/1.56      $i(v1) & $i(v0)) |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 4.97/1.56    (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | (
% 4.97/1.56          ~ (v2 = 0) &  ~ (v1 = 0)))) |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any]
% 4.97/1.56    : (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 =
% 4.97/1.56        0))
% 4.97/1.56  
% 4.97/1.56    (function-axioms)
% 4.97/1.56     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.97/1.56    [v3: $i] : (v1 = v0 |  ~ (rhasLeader(v3, v2) = v1) |  ~ (rhasLeader(v3, v2) =
% 4.97/1.56        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 4.97/1.56      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~ (rhasHead(v3,
% 4.97/1.56          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 4.97/1.56    ! [v2: $i] : (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0)) &
% 4.97/1.56     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 =
% 4.97/1.56      v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0)) &  ! [v0:
% 4.97/1.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 4.97/1.56      ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0)) &  ! [v0:
% 4.97/1.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 4.97/1.56      ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 4.97/1.56  
% 4.97/1.56  Those formulas are unsatisfiable:
% 4.97/1.56  ---------------------------------
% 4.97/1.56  
% 4.97/1.56  Begin of proof
% 4.97/1.56  | 
% 4.97/1.56  | ALPHA: (axiom_0) implies:
% 4.97/1.57  |   (1)   ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 4.97/1.57  |   (2)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~
% 4.97/1.57  |          $i(v0))
% 4.97/1.57  | 
% 4.97/1.57  | ALPHA: (axiom_1) implies:
% 4.97/1.57  |   (3)   ! [v0: $i] : ( ~ (xsd_string(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~
% 4.97/1.57  |            (v1 = 0) & xsd_integer(v0) = v1))
% 4.97/1.57  |   (4)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_string(v0) = v1) |  ~
% 4.97/1.57  |          $i(v0) | xsd_integer(v0) = 0)
% 4.97/1.57  | 
% 4.97/1.57  | ALPHA: (axiom_2) implies:
% 4.97/1.57  |   (5)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) |  ~ $i(v1) | 
% 4.97/1.57  |          ~ $i(v0) | rhasHead(v0, v1) = 0)
% 4.97/1.57  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasLeader(v0,
% 4.97/1.57  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) &
% 4.97/1.57  |            rhasHead(v0, v1) = v3))
% 4.97/1.57  | 
% 4.97/1.57  | ALPHA: (function-axioms) implies:
% 4.97/1.57  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.97/1.57  |        (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0))
% 4.97/1.57  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.97/1.57  |         ! [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~ (rhasHead(v3,
% 4.97/1.57  |              v2) = v0))
% 4.97/1.57  | 
% 4.97/1.57  | BETA: splitting (the_axiom) gives:
% 4.97/1.57  | 
% 4.97/1.57  | Case 1:
% 4.97/1.57  | | 
% 4.97/1.58  | |   (9)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58  | |          rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) = 0 & $i(v1) & $i(v0)) |
% 4.97/1.58  | |         ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58  | |          rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 & $i(v1) & $i(v0))
% 4.97/1.58  | | 
% 4.97/1.58  | | BETA: splitting (9) gives:
% 4.97/1.58  | | 
% 4.97/1.58  | | Case 1:
% 4.97/1.58  | | | 
% 4.97/1.58  | | |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58  | | |           rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) = 0 & $i(v1) &
% 4.97/1.58  | | |           $i(v0))
% 4.97/1.58  | | | 
% 4.97/1.58  | | | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1, all_12_2
% 4.97/1.58  | | |        gives:
% 4.97/1.58  | | |   (11)   ~ (all_12_0 = 0) & rhasLeader(all_12_2, all_12_1) = all_12_0 &
% 4.97/1.58  | | |         rhasHead(all_12_2, all_12_1) = 0 & $i(all_12_1) & $i(all_12_2)
% 4.97/1.58  | | | 
% 4.97/1.58  | | | ALPHA: (11) implies:
% 4.97/1.58  | | |   (12)   ~ (all_12_0 = 0)
% 4.97/1.58  | | |   (13)  $i(all_12_2)
% 4.97/1.58  | | |   (14)  $i(all_12_1)
% 4.97/1.58  | | |   (15)  rhasHead(all_12_2, all_12_1) = 0
% 4.97/1.58  | | |   (16)  rhasLeader(all_12_2, all_12_1) = all_12_0
% 4.97/1.58  | | | 
% 4.97/1.58  | | | GROUND_INST: instantiating (6) with all_12_2, all_12_1, all_12_0,
% 4.97/1.58  | | |              simplifying with (13), (14), (16) gives:
% 4.97/1.58  | | |   (17)  all_12_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_12_2,
% 4.97/1.58  | | |             all_12_1) = v0)
% 4.97/1.58  | | | 
% 4.97/1.58  | | | BETA: splitting (17) gives:
% 4.97/1.58  | | | 
% 4.97/1.58  | | | Case 1:
% 4.97/1.58  | | | | 
% 4.97/1.58  | | | |   (18)  all_12_0 = 0
% 4.97/1.58  | | | | 
% 4.97/1.58  | | | | REDUCE: (12), (18) imply:
% 4.97/1.58  | | | |   (19)  $false
% 5.66/1.58  | | | | 
% 5.66/1.58  | | | | CLOSE: (19) is inconsistent.
% 5.66/1.58  | | | | 
% 5.66/1.58  | | | Case 2:
% 5.66/1.58  | | | | 
% 5.66/1.58  | | | |   (20)   ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_12_2, all_12_1) = v0)
% 5.66/1.58  | | | | 
% 5.66/1.59  | | | | DELTA: instantiating (20) with fresh symbol all_21_0 gives:
% 5.66/1.59  | | | |   (21)   ~ (all_21_0 = 0) & rhasHead(all_12_2, all_12_1) = all_21_0
% 5.66/1.59  | | | | 
% 5.66/1.59  | | | | ALPHA: (21) implies:
% 5.66/1.59  | | | |   (22)   ~ (all_21_0 = 0)
% 5.66/1.59  | | | |   (23)  rhasHead(all_12_2, all_12_1) = all_21_0
% 5.66/1.59  | | | | 
% 5.66/1.59  | | | | GROUND_INST: instantiating (8) with 0, all_21_0, all_12_1, all_12_2,
% 5.66/1.59  | | | |              simplifying with (15), (23) gives:
% 5.66/1.59  | | | |   (24)  all_21_0 = 0
% 5.66/1.59  | | | | 
% 5.66/1.59  | | | | REDUCE: (22), (24) imply:
% 5.66/1.59  | | | |   (25)  $false
% 5.66/1.59  | | | | 
% 5.66/1.59  | | | | CLOSE: (25) is inconsistent.
% 5.66/1.59  | | | | 
% 5.66/1.59  | | | End of split
% 5.66/1.59  | | | 
% 5.66/1.59  | | Case 2:
% 5.66/1.59  | | | 
% 5.66/1.59  | | |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) &
% 5.66/1.59  | | |           rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 & $i(v1) &
% 5.66/1.59  | | |           $i(v0))
% 5.66/1.59  | | | 
% 5.66/1.59  | | | DELTA: instantiating (26) with fresh symbols all_12_0, all_12_1, all_12_2
% 5.66/1.59  | | |        gives:
% 5.66/1.59  | | |   (27)   ~ (all_12_0 = 0) & rhasLeader(all_12_2, all_12_1) = 0 &
% 5.66/1.59  | | |         rhasHead(all_12_2, all_12_1) = all_12_0 & $i(all_12_1) &
% 5.66/1.59  | | |         $i(all_12_2)
% 5.66/1.59  | | | 
% 5.66/1.59  | | | ALPHA: (27) implies:
% 5.66/1.59  | | |   (28)   ~ (all_12_0 = 0)
% 5.66/1.59  | | |   (29)  $i(all_12_2)
% 5.66/1.59  | | |   (30)  $i(all_12_1)
% 5.66/1.59  | | |   (31)  rhasHead(all_12_2, all_12_1) = all_12_0
% 5.66/1.59  | | |   (32)  rhasLeader(all_12_2, all_12_1) = 0
% 5.66/1.59  | | | 
% 5.66/1.59  | | | GROUND_INST: instantiating (5) with all_12_2, all_12_1, simplifying with
% 5.66/1.59  | | |              (29), (30), (32) gives:
% 5.66/1.59  | | |   (33)  rhasHead(all_12_2, all_12_1) = 0
% 5.66/1.59  | | | 
% 5.66/1.59  | | | GROUND_INST: instantiating (8) with all_12_0, 0, all_12_1, all_12_2,
% 5.66/1.59  | | |              simplifying with (31), (33) gives:
% 5.66/1.59  | | |   (34)  all_12_0 = 0
% 5.66/1.59  | | | 
% 5.66/1.59  | | | REDUCE: (28), (34) imply:
% 5.66/1.59  | | |   (35)  $false
% 5.66/1.59  | | | 
% 5.66/1.59  | | | CLOSE: (35) is inconsistent.
% 5.66/1.59  | | | 
% 5.66/1.59  | | End of split
% 5.66/1.59  | | 
% 5.66/1.59  | Case 2:
% 5.66/1.59  | | 
% 6.10/1.59  | |   (36)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (xsd_string(v0) = v1 &
% 6.10/1.59  | |           xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0)
% 6.10/1.59  | |               &  ~ (v1 = 0)))) |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 6.10/1.59  | |         (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) |
% 6.10/1.59  | |             v2 = 0))
% 6.10/1.59  | | 
% 6.10/1.59  | | BETA: splitting (36) gives:
% 6.10/1.59  | | 
% 6.10/1.59  | | Case 1:
% 6.10/1.59  | | | 
% 6.10/1.59  | | |   (37)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (xsd_string(v0) = v1 &
% 6.10/1.60  | | |           xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 =
% 6.10/1.60  | | |                 0) &  ~ (v1 = 0))))
% 6.10/1.60  | | | 
% 6.10/1.60  | | | DELTA: instantiating (37) with fresh symbols all_12_0, all_12_1, all_12_2
% 6.10/1.60  | | |        gives:
% 6.10/1.60  | | |   (38)  xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0
% 6.10/1.60  | | |         & $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 =
% 6.10/1.60  | | |               0) &  ~ (all_12_1 = 0)))
% 6.10/1.60  | | | 
% 6.10/1.60  | | | ALPHA: (38) implies:
% 6.10/1.60  | | |   (39)  $i(all_12_2)
% 6.10/1.60  | | |   (40)  xsd_integer(all_12_2) = all_12_0
% 6.10/1.60  | | |   (41)  xsd_string(all_12_2) = all_12_1
% 6.10/1.60  | | |   (42)  (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) &  ~ (all_12_1
% 6.10/1.60  | | |             = 0))
% 6.10/1.60  | | | 
% 6.10/1.60  | | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with
% 6.10/1.60  | | |              (39), (41) gives:
% 6.10/1.60  | | |   (43)  all_12_1 = 0 | xsd_integer(all_12_2) = 0
% 6.10/1.60  | | | 
% 6.10/1.60  | | | BETA: splitting (42) gives:
% 6.10/1.60  | | | 
% 6.10/1.60  | | | Case 1:
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | |   (44)  all_12_0 = 0 & all_12_1 = 0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | ALPHA: (44) implies:
% 6.10/1.60  | | | |   (45)  all_12_1 = 0
% 6.10/1.60  | | | |   (46)  all_12_0 = 0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | REDUCE: (41), (45) imply:
% 6.10/1.60  | | | |   (47)  xsd_string(all_12_2) = 0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | REDUCE: (40), (46) imply:
% 6.10/1.60  | | | |   (48)  xsd_integer(all_12_2) = 0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (39),
% 6.10/1.60  | | | |              (47) gives:
% 6.10/1.60  | | | |   (49)   ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0)
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | DELTA: instantiating (49) with fresh symbol all_26_0 gives:
% 6.10/1.60  | | | |   (50)   ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | ALPHA: (50) implies:
% 6.10/1.60  | | | |   (51)   ~ (all_26_0 = 0)
% 6.10/1.60  | | | |   (52)  xsd_integer(all_12_2) = all_26_0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | GROUND_INST: instantiating (7) with 0, all_26_0, all_12_2, simplifying
% 6.10/1.60  | | | |              with (48), (52) gives:
% 6.10/1.60  | | | |   (53)  all_26_0 = 0
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | REDUCE: (51), (53) imply:
% 6.10/1.60  | | | |   (54)  $false
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | CLOSE: (54) is inconsistent.
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | Case 2:
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | |   (55)   ~ (all_12_0 = 0) &  ~ (all_12_1 = 0)
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | ALPHA: (55) implies:
% 6.10/1.60  | | | |   (56)   ~ (all_12_1 = 0)
% 6.10/1.60  | | | |   (57)   ~ (all_12_0 = 0)
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | BETA: splitting (43) gives:
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | | Case 1:
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | |   (58)  xsd_integer(all_12_2) = 0
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | | GROUND_INST: instantiating (7) with all_12_0, 0, all_12_2, simplifying
% 6.10/1.60  | | | | |              with (40), (58) gives:
% 6.10/1.60  | | | | |   (59)  all_12_0 = 0
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | | REDUCE: (57), (59) imply:
% 6.10/1.60  | | | | |   (60)  $false
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | | CLOSE: (60) is inconsistent.
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | Case 2:
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | |   (61)  all_12_1 = 0
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | | REDUCE: (56), (61) imply:
% 6.10/1.60  | | | | |   (62)  $false
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | | CLOSE: (62) is inconsistent.
% 6.10/1.60  | | | | | 
% 6.10/1.60  | | | | End of split
% 6.10/1.60  | | | | 
% 6.10/1.60  | | | End of split
% 6.10/1.60  | | | 
% 6.10/1.60  | | Case 2:
% 6.10/1.60  | | | 
% 6.10/1.61  | | |   (63)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (cowlNothing(v0) = v2
% 6.10/1.61  | | |           & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 6.10/1.61  | | | 
% 6.10/1.61  | | | DELTA: instantiating (63) with fresh symbols all_12_0, all_12_1, all_12_2
% 6.10/1.61  | | |        gives:
% 6.10/1.61  | | |   (64)  cowlNothing(all_12_2) = all_12_0 & cowlThing(all_12_2) = all_12_1
% 6.10/1.61  | | |         & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0)
% 6.10/1.61  | | | 
% 6.10/1.61  | | | ALPHA: (64) implies:
% 6.10/1.61  | | |   (65)  $i(all_12_2)
% 6.10/1.61  | | |   (66)  cowlThing(all_12_2) = all_12_1
% 6.10/1.61  | | |   (67)  cowlNothing(all_12_2) = all_12_0
% 6.10/1.61  | | |   (68)   ~ (all_12_1 = 0) | all_12_0 = 0
% 6.10/1.61  | | | 
% 6.10/1.61  | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with
% 6.10/1.61  | | |              (65), (66) gives:
% 6.10/1.61  | | |   (69)  all_12_1 = 0
% 6.10/1.61  | | | 
% 6.10/1.61  | | | BETA: splitting (68) gives:
% 6.10/1.61  | | | 
% 6.10/1.61  | | | Case 1:
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | |   (70)   ~ (all_12_1 = 0)
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | | REDUCE: (69), (70) imply:
% 6.10/1.61  | | | |   (71)  $false
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | | CLOSE: (71) is inconsistent.
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | Case 2:
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | |   (72)  all_12_0 = 0
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | | REDUCE: (67), (72) imply:
% 6.10/1.61  | | | |   (73)  cowlNothing(all_12_2) = 0
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (65),
% 6.10/1.61  | | | |              (73) gives:
% 6.10/1.61  | | | |   (74)  $false
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | | CLOSE: (74) is inconsistent.
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | End of split
% 6.10/1.61  | | | 
% 6.10/1.61  | | End of split
% 6.10/1.61  | | 
% 6.10/1.61  | End of split
% 6.10/1.61  | 
% 6.10/1.61  End of proof
% 6.10/1.61  % SZS output end Proof for theBenchmark
% 6.10/1.61  
% 6.10/1.61  1003ms
%------------------------------------------------------------------------------