TSTP Solution File: SYN729+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN729+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n020.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 : Fri Sep  1 03:28:44 EDT 2023

% Result   : Theorem 3.99s 1.39s
% Output   : Proof 6.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYN729+1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35  % Computer : n020.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Sat Aug 26 17:18:59 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.22/0.61  ________       _____
% 0.22/0.61  ___  __ \_________(_)________________________________
% 0.22/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61  
% 0.22/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61  (2023-06-19)
% 0.22/0.61  
% 0.22/0.61  (c) Philipp Rümmer, 2009-2023
% 0.22/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61                Amanda Stjerna.
% 0.22/0.61  Free software under BSD-3-Clause.
% 0.22/0.61  
% 0.22/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61  
% 0.22/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.62  Running up to 7 provers in parallel.
% 0.22/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.06/0.98  Prover 1: Preprocessing ...
% 2.06/0.98  Prover 4: Preprocessing ...
% 2.19/1.02  Prover 0: Preprocessing ...
% 2.19/1.02  Prover 3: Preprocessing ...
% 2.19/1.02  Prover 5: Preprocessing ...
% 2.19/1.02  Prover 2: Preprocessing ...
% 2.19/1.02  Prover 6: Preprocessing ...
% 3.00/1.12  Prover 1: Constructing countermodel ...
% 3.00/1.12  Prover 3: Constructing countermodel ...
% 3.00/1.13  Prover 6: Proving ...
% 3.00/1.13  Prover 2: Proving ...
% 3.00/1.13  Prover 5: Proving ...
% 3.00/1.14  Prover 4: Constructing countermodel ...
% 3.00/1.15  Prover 0: Proving ...
% 3.99/1.39  Prover 0: proved (745ms)
% 3.99/1.39  
% 3.99/1.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/1.39  
% 3.99/1.39  Prover 3: stopped
% 3.99/1.39  Prover 5: stopped
% 3.99/1.40  Prover 2: stopped
% 3.99/1.40  Prover 6: stopped
% 3.99/1.40  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.99/1.40  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.99/1.40  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.99/1.40  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.99/1.40  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.99/1.41  Prover 10: Preprocessing ...
% 3.99/1.43  Prover 7: Preprocessing ...
% 3.99/1.43  Prover 8: Preprocessing ...
% 3.99/1.43  Prover 11: Preprocessing ...
% 3.99/1.43  Prover 13: Preprocessing ...
% 5.06/1.46  Prover 8: Warning: ignoring some quantifiers
% 5.06/1.47  Prover 8: Constructing countermodel ...
% 5.29/1.47  Prover 10: Warning: ignoring some quantifiers
% 5.29/1.48  Prover 13: Warning: ignoring some quantifiers
% 5.29/1.48  Prover 10: Constructing countermodel ...
% 5.29/1.48  Prover 13: Constructing countermodel ...
% 5.29/1.49  Prover 7: Warning: ignoring some quantifiers
% 5.29/1.49  Prover 7: Constructing countermodel ...
% 5.29/1.50  Prover 10: gave up
% 5.29/1.52  Prover 7: gave up
% 5.29/1.52  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.29/1.52  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.29/1.53  Prover 11: Constructing countermodel ...
% 5.29/1.53  Prover 19: Preprocessing ...
% 5.29/1.54  Prover 16: Preprocessing ...
% 5.29/1.56  Prover 4: Found proof (size 31)
% 5.29/1.56  Prover 4: proved (917ms)
% 5.29/1.56  Prover 8: stopped
% 5.29/1.56  Prover 13: stopped
% 5.29/1.56  Prover 16: Warning: ignoring some quantifiers
% 5.29/1.56  Prover 11: stopped
% 5.29/1.56  Prover 1: stopped
% 5.29/1.56  Prover 16: Constructing countermodel ...
% 5.29/1.56  Prover 16: stopped
% 6.13/1.60  Prover 19: Warning: ignoring some quantifiers
% 6.13/1.60  Prover 19: Constructing countermodel ...
% 6.13/1.61  Prover 19: stopped
% 6.13/1.61  
% 6.13/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.13/1.61  
% 6.13/1.62  % SZS output start Proof for theBenchmark
% 6.13/1.62  Assumptions after simplification:
% 6.13/1.62  ---------------------------------
% 6.26/1.62  
% 6.26/1.62    (thm72)
% 6.28/1.68     ? [v0: $i] : (p(v0) = 0 & $i(v0) &  ! [v1: $i] :  ! [v2: $i] : ( ~ (h(v1) =
% 6.28/1.68          v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: $i] :  ? [v5: any] :  ? [v6:
% 6.28/1.68          any] : (g(v1) = v4 & p(v4) = v5 & p(v2) = v6 & p(v1) = v3 & $i(v4) & ( ~
% 6.28/1.68            (v3 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v1: $i] :  ! [v2: $i] : ( ~
% 6.28/1.68        (g(v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :  ?
% 6.28/1.68        [v6: any] : (h(v1) = v5 & p(v5) = v6 & p(v2) = v4 & p(v1) = v3 & $i(v5) &
% 6.28/1.68          ( ~ (v3 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v1: $i] :  ! [v2: any] : ( ~
% 6.28/1.68        (p(v1) = v2) |  ~ $i(v1) |  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ?
% 6.28/1.68        [v6: any] :  ? [v7: any] : (h(v3) = v4 & g(v4) = v5 & l(v1, v5) = v6 &
% 6.28/1.68          p(v3) = v7 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v7 = 0 & v6 =
% 6.28/1.68              0)))) &  ! [v1: $i] : ( ~ (l(v0, v1) = 0) |  ~ $i(v1) |  ? [v2: int]
% 6.28/1.68        : ( ~ (v2 = 0) & p(v1) = v2)) &  ! [v1: $i] : ( ~ (p(v1) = 0) |  ~ $i(v1)
% 6.28/1.68        |  ? [v2: $i] :  ? [v3: $i] : (h(v1) = v3 & g(v1) = v2 & p(v3) = 0 & p(v2)
% 6.28/1.68          = 0 & $i(v3) & $i(v2))) &  ! [v1: $i] : ( ~ (p(v1) = 0) |  ~ $i(v1) |  ?
% 6.28/1.68        [v2: int] : ( ~ (v2 = 0) & l(v0, v1) = v2)))
% 6.28/1.68  
% 6.28/1.68    (function-axioms)
% 6.28/1.69     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 6.28/1.69    [v3: $i] : (v1 = v0 |  ~ (l(v3, v2) = v1) |  ~ (l(v3, v2) = v0)) &  ! [v0: $i]
% 6.28/1.69    :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (h(v2) = v1) |  ~ (h(v2) = v0)) & 
% 6.28/1.69    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (g(v2) = v1) |  ~
% 6.28/1.69      (g(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  !
% 6.28/1.69    [v2: $i] : (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 6.28/1.69  
% 6.28/1.69  Those formulas are unsatisfiable:
% 6.28/1.69  ---------------------------------
% 6.28/1.69  
% 6.28/1.69  Begin of proof
% 6.28/1.69  | 
% 6.28/1.69  | ALPHA: (function-axioms) implies:
% 6.28/1.69  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.28/1.69  |        (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 6.28/1.69  | 
% 6.28/1.69  | DELTA: instantiating (thm72) with fresh symbol all_3_0 gives:
% 6.63/1.71  |   (2)  p(all_3_0) = 0 & $i(all_3_0) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (h(v0) =
% 6.63/1.71  |            v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: $i] :  ? [v4: any] :  ?
% 6.63/1.71  |          [v5: any] : (g(v0) = v3 & p(v3) = v4 & p(v1) = v5 & p(v0) = v2 &
% 6.63/1.71  |            $i(v3) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) &  ! [v0: $i] :  !
% 6.63/1.71  |        [v1: $i] : ( ~ (g(v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] :
% 6.63/1.71  |           ? [v4: $i] :  ? [v5: any] : (h(v0) = v4 & p(v4) = v5 & p(v1) = v3 &
% 6.63/1.71  |            p(v0) = v2 & $i(v4) & ( ~ (v2 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0:
% 6.63/1.71  |          $i] :  ! [v1: any] : ( ~ (p(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :  ?
% 6.63/1.71  |          [v3: $i] :  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] : (h(v2) = v3 &
% 6.63/1.71  |            g(v3) = v4 & l(v0, v4) = v5 & p(v2) = v6 & $i(v4) & $i(v3) & $i(v2)
% 6.63/1.71  |            & ( ~ (v1 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0: $i] : ( ~
% 6.63/1.71  |          (l(all_3_0, v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) &
% 6.63/1.71  |            p(v0) = v1)) &  ! [v0: $i] : ( ~ (p(v0) = 0) |  ~ $i(v0) |  ? [v1:
% 6.63/1.71  |            $i] :  ? [v2: $i] : (h(v0) = v2 & g(v0) = v1 & p(v2) = 0 & p(v1) =
% 6.63/1.71  |            0 & $i(v2) & $i(v1))) &  ! [v0: $i] : ( ~ (p(v0) = 0) |  ~ $i(v0) |
% 6.63/1.71  |           ? [v1: int] : ( ~ (v1 = 0) & l(all_3_0, v0) = v1))
% 6.63/1.71  | 
% 6.63/1.71  | ALPHA: (2) implies:
% 6.63/1.71  |   (3)  $i(all_3_0)
% 6.63/1.71  |   (4)  p(all_3_0) = 0
% 6.63/1.72  |   (5)   ! [v0: $i] : ( ~ (l(all_3_0, v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~
% 6.63/1.72  |            (v1 = 0) & p(v0) = v1))
% 6.63/1.72  |   (6)   ! [v0: $i] :  ! [v1: any] : ( ~ (p(v0) = v1) |  ~ $i(v0) |  ? [v2: $i]
% 6.63/1.72  |          :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: any] :  ? [v6: any] : (h(v2) =
% 6.63/1.72  |            v3 & g(v3) = v4 & l(v0, v4) = v5 & p(v2) = v6 & $i(v4) & $i(v3) &
% 6.63/1.72  |            $i(v2) & ( ~ (v1 = 0) | (v6 = 0 & v5 = 0))))
% 6.63/1.72  |   (7)   ! [v0: $i] :  ! [v1: $i] : ( ~ (g(v0) = v1) |  ~ $i(v0) |  ? [v2: any]
% 6.63/1.72  |          :  ? [v3: any] :  ? [v4: $i] :  ? [v5: any] : (h(v0) = v4 & p(v4) =
% 6.63/1.72  |            v5 & p(v1) = v3 & p(v0) = v2 & $i(v4) & ( ~ (v2 = 0) | (v5 = 0 & v3
% 6.63/1.72  |                = 0))))
% 6.63/1.72  |   (8)   ! [v0: $i] :  ! [v1: $i] : ( ~ (h(v0) = v1) |  ~ $i(v0) |  ? [v2: any]
% 6.63/1.72  |          :  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] : (g(v0) = v3 & p(v3) =
% 6.63/1.72  |            v4 & p(v1) = v5 & p(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v5 = 0 & v4
% 6.63/1.72  |                = 0))))
% 6.63/1.72  | 
% 6.63/1.73  | GROUND_INST: instantiating (6) with all_3_0, 0, simplifying with (3), (4)
% 6.63/1.73  |              gives:
% 6.63/1.73  |   (9)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (h(v0) = v1 & g(v1) = v2 &
% 6.63/1.73  |          l(all_3_0, v2) = 0 & p(v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 6.63/1.73  | 
% 6.63/1.73  | DELTA: instantiating (9) with fresh symbols all_15_0, all_15_1, all_15_2
% 6.63/1.73  |        gives:
% 6.63/1.73  |   (10)  h(all_15_2) = all_15_1 & g(all_15_1) = all_15_0 & l(all_3_0, all_15_0)
% 6.63/1.73  |         = 0 & p(all_15_2) = 0 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2)
% 6.63/1.73  | 
% 6.63/1.73  | ALPHA: (10) implies:
% 6.63/1.73  |   (11)  $i(all_15_2)
% 6.63/1.73  |   (12)  $i(all_15_1)
% 6.63/1.73  |   (13)  $i(all_15_0)
% 6.63/1.73  |   (14)  p(all_15_2) = 0
% 6.63/1.73  |   (15)  l(all_3_0, all_15_0) = 0
% 6.63/1.73  |   (16)  g(all_15_1) = all_15_0
% 6.63/1.73  |   (17)  h(all_15_2) = all_15_1
% 6.63/1.73  | 
% 6.63/1.73  | GROUND_INST: instantiating (5) with all_15_0, simplifying with (13), (15)
% 6.63/1.73  |              gives:
% 6.63/1.73  |   (18)   ? [v0: int] : ( ~ (v0 = 0) & p(all_15_0) = v0)
% 6.63/1.73  | 
% 6.63/1.73  | GROUND_INST: instantiating (7) with all_15_1, all_15_0, simplifying with (12),
% 6.63/1.73  |              (16) gives:
% 6.63/1.73  |   (19)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: any] :
% 6.63/1.73  |         (h(all_15_1) = v2 & p(v2) = v3 & p(all_15_0) = v1 & p(all_15_1) = v0 &
% 6.63/1.73  |           $i(v2) & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 6.63/1.73  | 
% 6.63/1.74  | GROUND_INST: instantiating (8) with all_15_2, all_15_1, simplifying with (11),
% 6.63/1.74  |              (17) gives:
% 6.63/1.74  |   (20)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] :  ? [v3: any] :
% 6.63/1.74  |         (g(all_15_2) = v1 & p(v1) = v2 & p(all_15_1) = v3 & p(all_15_2) = v0 &
% 6.63/1.74  |           $i(v1) & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 6.63/1.74  | 
% 6.63/1.74  | DELTA: instantiating (18) with fresh symbol all_22_0 gives:
% 6.63/1.74  |   (21)   ~ (all_22_0 = 0) & p(all_15_0) = all_22_0
% 6.63/1.74  | 
% 6.63/1.74  | ALPHA: (21) implies:
% 6.63/1.74  |   (22)   ~ (all_22_0 = 0)
% 6.63/1.74  |   (23)  p(all_15_0) = all_22_0
% 6.63/1.74  | 
% 6.63/1.74  | DELTA: instantiating (20) with fresh symbols all_42_0, all_42_1, all_42_2,
% 6.63/1.74  |        all_42_3 gives:
% 6.63/1.74  |   (24)  g(all_15_2) = all_42_2 & p(all_42_2) = all_42_1 & p(all_15_1) =
% 6.63/1.74  |         all_42_0 & p(all_15_2) = all_42_3 & $i(all_42_2) & ( ~ (all_42_3 = 0)
% 6.63/1.74  |           | (all_42_0 = 0 & all_42_1 = 0))
% 6.63/1.74  | 
% 6.63/1.74  | ALPHA: (24) implies:
% 6.63/1.74  |   (25)  p(all_15_2) = all_42_3
% 6.63/1.74  |   (26)  p(all_15_1) = all_42_0
% 6.63/1.74  |   (27)   ~ (all_42_3 = 0) | (all_42_0 = 0 & all_42_1 = 0)
% 6.63/1.74  | 
% 6.63/1.74  | DELTA: instantiating (19) with fresh symbols all_44_0, all_44_1, all_44_2,
% 6.63/1.74  |        all_44_3 gives:
% 6.63/1.74  |   (28)  h(all_15_1) = all_44_1 & p(all_44_1) = all_44_0 & p(all_15_0) =
% 6.63/1.74  |         all_44_2 & p(all_15_1) = all_44_3 & $i(all_44_1) & ( ~ (all_44_3 = 0)
% 6.63/1.74  |           | (all_44_0 = 0 & all_44_2 = 0))
% 6.63/1.74  | 
% 6.63/1.74  | ALPHA: (28) implies:
% 6.63/1.74  |   (29)  p(all_15_1) = all_44_3
% 6.63/1.74  |   (30)  p(all_15_0) = all_44_2
% 6.63/1.74  |   (31)   ~ (all_44_3 = 0) | (all_44_0 = 0 & all_44_2 = 0)
% 6.63/1.74  | 
% 6.63/1.74  | GROUND_INST: instantiating (1) with 0, all_42_3, all_15_2, simplifying with
% 6.63/1.74  |              (14), (25) gives:
% 6.63/1.74  |   (32)  all_42_3 = 0
% 6.63/1.74  | 
% 6.63/1.74  | GROUND_INST: instantiating (1) with all_42_0, all_44_3, all_15_1, simplifying
% 6.63/1.74  |              with (26), (29) gives:
% 6.63/1.74  |   (33)  all_44_3 = all_42_0
% 6.63/1.75  | 
% 6.63/1.75  | GROUND_INST: instantiating (1) with all_22_0, all_44_2, all_15_0, simplifying
% 6.63/1.75  |              with (23), (30) gives:
% 6.63/1.75  |   (34)  all_44_2 = all_22_0
% 6.63/1.75  | 
% 6.63/1.75  | BETA: splitting (31) gives:
% 6.63/1.75  | 
% 6.63/1.75  | Case 1:
% 6.63/1.75  | | 
% 6.63/1.75  | |   (35)   ~ (all_44_3 = 0)
% 6.63/1.75  | | 
% 6.63/1.75  | | REDUCE: (33), (35) imply:
% 6.63/1.75  | |   (36)   ~ (all_42_0 = 0)
% 6.63/1.75  | | 
% 6.63/1.75  | | BETA: splitting (27) gives:
% 6.63/1.75  | | 
% 6.63/1.75  | | Case 1:
% 6.63/1.75  | | | 
% 6.63/1.75  | | |   (37)   ~ (all_42_3 = 0)
% 6.63/1.75  | | | 
% 6.63/1.75  | | | REDUCE: (32), (37) imply:
% 6.63/1.75  | | |   (38)  $false
% 6.63/1.75  | | | 
% 6.63/1.75  | | | CLOSE: (38) is inconsistent.
% 6.63/1.75  | | | 
% 6.63/1.75  | | Case 2:
% 6.63/1.75  | | | 
% 6.63/1.75  | | |   (39)  all_42_0 = 0 & all_42_1 = 0
% 6.63/1.75  | | | 
% 6.63/1.75  | | | ALPHA: (39) implies:
% 6.63/1.75  | | |   (40)  all_42_0 = 0
% 6.63/1.75  | | | 
% 6.63/1.75  | | | REDUCE: (36), (40) imply:
% 6.63/1.75  | | |   (41)  $false
% 6.63/1.75  | | | 
% 6.63/1.75  | | | CLOSE: (41) is inconsistent.
% 6.63/1.75  | | | 
% 6.63/1.75  | | End of split
% 6.63/1.75  | | 
% 6.63/1.75  | Case 2:
% 6.63/1.75  | | 
% 6.63/1.75  | |   (42)  all_44_0 = 0 & all_44_2 = 0
% 6.63/1.75  | | 
% 6.63/1.75  | | ALPHA: (42) implies:
% 6.63/1.75  | |   (43)  all_44_2 = 0
% 6.63/1.75  | | 
% 6.63/1.75  | | COMBINE_EQS: (34), (43) imply:
% 6.63/1.75  | |   (44)  all_22_0 = 0
% 6.63/1.75  | | 
% 6.63/1.75  | | SIMP: (44) implies:
% 6.63/1.75  | |   (45)  all_22_0 = 0
% 6.63/1.75  | | 
% 6.63/1.75  | | REDUCE: (22), (45) imply:
% 6.63/1.75  | |   (46)  $false
% 6.63/1.75  | | 
% 6.63/1.75  | | CLOSE: (46) is inconsistent.
% 6.63/1.75  | | 
% 6.63/1.75  | End of split
% 6.63/1.75  | 
% 6.63/1.75  End of proof
% 6.63/1.75  % SZS output end Proof for theBenchmark
% 6.63/1.75  
% 6.63/1.75  1137ms
%------------------------------------------------------------------------------