TSTP Solution File: DAT051_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : DAT051_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n018.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 : Wed Aug 30 22:19:01 EDT 2023

% Result   : Theorem 7.85s 1.79s
% Output   : Proof 10.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT051_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug 24 14:50:27 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.06/1.15  Prover 4: Preprocessing ...
% 3.06/1.15  Prover 3: Preprocessing ...
% 3.06/1.15  Prover 2: Preprocessing ...
% 3.06/1.15  Prover 6: Preprocessing ...
% 3.06/1.15  Prover 5: Preprocessing ...
% 3.06/1.15  Prover 0: Preprocessing ...
% 3.06/1.15  Prover 1: Preprocessing ...
% 4.74/1.41  Prover 6: Constructing countermodel ...
% 4.74/1.41  Prover 3: Constructing countermodel ...
% 4.74/1.42  Prover 1: Constructing countermodel ...
% 4.74/1.48  Prover 2: Proving ...
% 5.01/1.50  Prover 0: Proving ...
% 5.01/1.51  Prover 5: Proving ...
% 5.01/1.53  Prover 4: Constructing countermodel ...
% 7.59/1.78  Prover 6: proved (1142ms)
% 7.59/1.78  
% 7.85/1.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.85/1.79  
% 7.85/1.79  Prover 3: proved (1151ms)
% 7.85/1.79  
% 7.85/1.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.85/1.79  
% 7.85/1.79  Prover 0: stopped
% 7.85/1.79  Prover 5: stopped
% 7.85/1.79  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.85/1.79  Prover 2: stopped
% 7.85/1.80  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.85/1.80  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.85/1.80  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.85/1.82  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.18/1.84  Prover 8: Preprocessing ...
% 8.27/1.85  Prover 7: Preprocessing ...
% 8.27/1.86  Prover 10: Preprocessing ...
% 8.27/1.86  Prover 13: Preprocessing ...
% 8.27/1.88  Prover 11: Preprocessing ...
% 8.27/1.90  Prover 7: Constructing countermodel ...
% 8.78/1.94  Prover 8: Warning: ignoring some quantifiers
% 8.78/1.95  Prover 8: Constructing countermodel ...
% 8.78/1.95  Prover 10: Constructing countermodel ...
% 9.12/1.96  Prover 13: Warning: ignoring some quantifiers
% 9.12/1.97  Prover 13: Constructing countermodel ...
% 9.12/2.03  Prover 11: Constructing countermodel ...
% 9.12/2.15  Prover 10: Found proof (size 64)
% 9.12/2.15  Prover 10: proved (348ms)
% 9.12/2.15  Prover 11: stopped
% 9.12/2.15  Prover 7: stopped
% 9.12/2.15  Prover 13: stopped
% 9.12/2.15  Prover 8: stopped
% 9.12/2.15  Prover 1: stopped
% 9.12/2.15  Prover 4: stopped
% 9.12/2.15  
% 9.12/2.15  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.12/2.15  
% 9.87/2.17  % SZS output start Proof for theBenchmark
% 9.87/2.17  Assumptions after simplification:
% 9.87/2.17  ---------------------------------
% 9.87/2.17  
% 9.87/2.17    (ax11)
% 9.87/2.19     ! [v0: record] :  ! [v1: record] : ( ~ (split2(v0) = v1) |  ~ record(v0) |  ~
% 9.87/2.19      isrecord(v0) | isrecord(v1) |  ? [v2: record] : (next(v0) = v2 & record(v2)
% 9.87/2.19        &  ~ isrecord(v2)))
% 9.87/2.19  
% 9.87/2.19    (ax12)
% 9.87/2.19     ! [v0: record] :  ! [v1: record] : ( ~ (split2(v0) = v1) |  ~ record(v0) |  ~
% 9.87/2.19      isrecord(v0) |  ? [v2: record] :  ? [v3: int] :  ? [v4: int] : (next(v0) =
% 9.87/2.19        v2 & record(v2) & ( ~ isrecord(v2) | (v4 = v3 & data(v2) = v3 & data(v1) =
% 9.87/2.19            v3))))
% 9.87/2.19  
% 9.87/2.19    (ax13)
% 9.87/2.19     ! [v0: record] :  ! [v1: record] : ( ~ (split2(v0) = v1) |  ~ record(v0) |  ~
% 9.87/2.19      isrecord(v0) |  ? [v2: record] :  ? [v3: record] :  ? [v4: record] :  ? [v5:
% 9.87/2.19        record] : (next(v0) = v2 & record(v2) & ( ~ isrecord(v2) | (v5 = v3 &
% 9.87/2.19            split2(v4) = v3 & next(v2) = v4 & next(v1) = v3 & record(v4) &
% 9.87/2.19            record(v3)))))
% 9.87/2.19  
% 9.87/2.19    (ax3)
% 9.87/2.19     ! [v0: record] :  ! [v1: int] : ( ~ (length(v0) = v1) |  ~ record(v0) |  ~
% 9.87/2.19      isrecord(v0) |  ? [v2: record] : (next(v0) = v2 & length(v2) = $sum(v1, -1)
% 9.87/2.19        & record(v2)))
% 9.87/2.19  
% 9.87/2.19    (co1)
% 9.87/2.19     ? [v0: record] :  ? [v1: record] :  ? [v2: record] :  ? [v3: record] :  ?
% 9.87/2.19    [v4: int] :  ? [v5: int] :  ? [v6: record] :  ? [v7: int] :  ? [v8: int] : ( ~
% 9.87/2.19      ($difference(v8, $product(2, v7)) = 1) &  ~ (v8 = $product(2, v7)) &
% 9.87/2.19      split2(v1) = v3 & split2(v0) = v6 & next(v2) = v1 & next(v0) = v2 &
% 10.70/2.19      length(v6) = v7 & length(v3) = v4 & length(v1) = v5 & length(v0) = v8 &
% 10.70/2.19      record(v6) & record(v3) & record(v2) & record(v1) & record(v0) &
% 10.70/2.19      isrecord(v2) & isrecord(v0) & ($difference(v5, $product(2, v4)) = 1 | v5 =
% 10.70/2.19        $product(2, v4)))
% 10.70/2.19  
% 10.70/2.19    (function-axioms)
% 10.70/2.20     ! [v0: record] :  ! [v1: record] :  ! [v2: record] : (v1 = v0 |  ~
% 10.70/2.20      (split2(v2) = v1) |  ~ (split2(v2) = v0)) &  ! [v0: int] :  ! [v1: int] :  !
% 10.70/2.20    [v2: record] : (v1 = v0 |  ~ (data(v2) = v1) |  ~ (data(v2) = v0)) &  ! [v0:
% 10.70/2.20      record] :  ! [v1: record] :  ! [v2: record] : (v1 = v0 |  ~ (split1(v2) =
% 10.70/2.20        v1) |  ~ (split1(v2) = v0)) &  ! [v0: record] :  ! [v1: record] :  ! [v2:
% 10.70/2.20      record] : (v1 = v0 |  ~ (next(v2) = v1) |  ~ (next(v2) = v0)) &  ! [v0: int]
% 10.70/2.20    :  ! [v1: int] :  ! [v2: record] : (v1 = v0 |  ~ (length(v2) = v1) |  ~
% 10.70/2.20      (length(v2) = v0))
% 10.70/2.20  
% 10.70/2.20  Further assumptions not needed in the proof:
% 10.70/2.20  --------------------------------------------
% 10.70/2.20  ax1, ax10, ax2, ax4, ax5, ax6, ax7, ax8, ax9
% 10.70/2.20  
% 10.70/2.20  Those formulas are unsatisfiable:
% 10.70/2.20  ---------------------------------
% 10.70/2.20  
% 10.70/2.20  Begin of proof
% 10.70/2.20  | 
% 10.70/2.20  | ALPHA: (function-axioms) implies:
% 10.70/2.20  |   (1)   ! [v0: int] :  ! [v1: int] :  ! [v2: record] : (v1 = v0 |  ~
% 10.70/2.20  |          (length(v2) = v1) |  ~ (length(v2) = v0))
% 10.70/2.20  |   (2)   ! [v0: record] :  ! [v1: record] :  ! [v2: record] : (v1 = v0 |  ~
% 10.70/2.20  |          (next(v2) = v1) |  ~ (next(v2) = v0))
% 10.70/2.20  |   (3)   ! [v0: record] :  ! [v1: record] :  ! [v2: record] : (v1 = v0 |  ~
% 10.70/2.20  |          (split2(v2) = v1) |  ~ (split2(v2) = v0))
% 10.70/2.20  | 
% 10.70/2.20  | DELTA: instantiating (co1) with fresh symbols all_18_0, all_18_1, all_18_2,
% 10.70/2.20  |        all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8 gives:
% 10.70/2.21  |   (4)   ~ ($difference(all_18_0, $product(2, all_18_1)) = 1) &  ~ (all_18_0 =
% 10.70/2.21  |          $product(2, all_18_1)) & split2(all_18_7) = all_18_5 &
% 10.70/2.21  |        split2(all_18_8) = all_18_2 & next(all_18_6) = all_18_7 &
% 10.70/2.21  |        next(all_18_8) = all_18_6 & length(all_18_2) = all_18_1 &
% 10.70/2.21  |        length(all_18_5) = all_18_4 & length(all_18_7) = all_18_3 &
% 10.70/2.21  |        length(all_18_8) = all_18_0 & record(all_18_2) & record(all_18_5) &
% 10.70/2.21  |        record(all_18_6) & record(all_18_7) & record(all_18_8) &
% 10.70/2.21  |        isrecord(all_18_6) & isrecord(all_18_8) & ($difference(all_18_3,
% 10.70/2.21  |            $product(2, all_18_4)) = 1 | all_18_3 = $product(2, all_18_4))
% 10.70/2.21  | 
% 10.70/2.21  | ALPHA: (4) implies:
% 10.70/2.21  |   (5)   ~ (all_18_0 = $product(2, all_18_1))
% 10.70/2.21  |   (6)   ~ ($difference(all_18_0, $product(2, all_18_1)) = 1)
% 10.70/2.21  |   (7)  isrecord(all_18_8)
% 10.70/2.21  |   (8)  isrecord(all_18_6)
% 10.70/2.21  |   (9)  record(all_18_8)
% 10.70/2.21  |   (10)  record(all_18_2)
% 10.70/2.21  |   (11)  length(all_18_8) = all_18_0
% 10.70/2.21  |   (12)  length(all_18_7) = all_18_3
% 10.70/2.21  |   (13)  length(all_18_5) = all_18_4
% 10.70/2.21  |   (14)  length(all_18_2) = all_18_1
% 10.70/2.21  |   (15)  next(all_18_8) = all_18_6
% 10.70/2.21  |   (16)  next(all_18_6) = all_18_7
% 10.70/2.21  |   (17)  split2(all_18_8) = all_18_2
% 10.70/2.21  |   (18)  split2(all_18_7) = all_18_5
% 10.70/2.21  |   (19)  $difference(all_18_3, $product(2, all_18_4)) = 1 | all_18_3 =
% 10.70/2.21  |         $product(2, all_18_4)
% 10.70/2.21  | 
% 10.70/2.21  | GROUND_INST: instantiating (ax3) with all_18_8, all_18_0, simplifying with
% 10.70/2.21  |              (7), (9), (11) gives:
% 10.70/2.21  |   (20)   ? [v0: record] : (next(all_18_8) = v0 & length(v0) = $sum(all_18_0,
% 10.70/2.21  |             -1) & record(v0))
% 10.70/2.21  | 
% 10.70/2.21  | GROUND_INST: instantiating (ax11) with all_18_8, all_18_2, simplifying with
% 10.70/2.21  |              (7), (9), (17) gives:
% 10.70/2.21  |   (21)  isrecord(all_18_2) |  ? [v0: record] : (next(all_18_8) = v0 &
% 10.70/2.21  |           record(v0) &  ~ isrecord(v0))
% 10.70/2.21  | 
% 10.70/2.21  | GROUND_INST: instantiating (ax13) with all_18_8, all_18_2, simplifying with
% 10.70/2.21  |              (7), (9), (17) gives:
% 10.70/2.21  |   (22)   ? [v0: record] :  ? [v1: record] :  ? [v2: record] :  ? [v3: record]
% 10.70/2.21  |         : (next(all_18_8) = v0 & record(v0) & ( ~ isrecord(v0) | (v3 = v1 &
% 10.70/2.21  |               split2(v2) = v1 & next(v0) = v2 & next(all_18_2) = v1 &
% 10.70/2.21  |               record(v2) & record(v1))))
% 10.70/2.21  | 
% 10.70/2.21  | GROUND_INST: instantiating (ax12) with all_18_8, all_18_2, simplifying with
% 10.70/2.21  |              (7), (9), (17) gives:
% 10.70/2.22  |   (23)   ? [v0: record] :  ? [v1: int] :  ? [v2: int] : (next(all_18_8) = v0 &
% 10.70/2.22  |           record(v0) & ( ~ isrecord(v0) | (v2 = v1 & data(v0) = v1 &
% 10.70/2.22  |               data(all_18_2) = v1)))
% 10.70/2.22  | 
% 10.70/2.22  | DELTA: instantiating (20) with fresh symbol all_27_0 gives:
% 10.70/2.22  |   (24)  next(all_18_8) = all_27_0 & length(all_27_0) = $sum(all_18_0, -1) &
% 10.70/2.22  |         record(all_27_0)
% 10.70/2.22  | 
% 10.70/2.22  | ALPHA: (24) implies:
% 10.70/2.22  |   (25)  record(all_27_0)
% 10.70/2.22  |   (26)  length(all_27_0) = $sum(all_18_0, -1)
% 10.70/2.22  |   (27)  next(all_18_8) = all_27_0
% 10.70/2.22  | 
% 10.70/2.22  | DELTA: instantiating (23) with fresh symbols all_29_0, all_29_1, all_29_2
% 10.70/2.22  |        gives:
% 10.70/2.22  |   (28)  next(all_18_8) = all_29_2 & record(all_29_2) & ( ~ isrecord(all_29_2)
% 10.70/2.22  |           | (all_29_0 = all_29_1 & data(all_29_2) = all_29_1 & data(all_18_2)
% 10.70/2.22  |             = all_29_1))
% 10.70/2.22  | 
% 10.70/2.22  | ALPHA: (28) implies:
% 10.70/2.22  |   (29)  next(all_18_8) = all_29_2
% 10.70/2.22  | 
% 10.70/2.22  | DELTA: instantiating (22) with fresh symbols all_31_0, all_31_1, all_31_2,
% 10.70/2.22  |        all_31_3 gives:
% 10.70/2.22  |   (30)  next(all_18_8) = all_31_3 & record(all_31_3) & ( ~ isrecord(all_31_3)
% 10.70/2.22  |           | (all_31_0 = all_31_2 & split2(all_31_1) = all_31_2 &
% 10.70/2.22  |             next(all_31_3) = all_31_1 & next(all_18_2) = all_31_2 &
% 10.70/2.22  |             record(all_31_1) & record(all_31_2)))
% 10.70/2.22  | 
% 10.70/2.22  | ALPHA: (30) implies:
% 10.70/2.22  |   (31)  next(all_18_8) = all_31_3
% 10.70/2.22  |   (32)   ~ isrecord(all_31_3) | (all_31_0 = all_31_2 & split2(all_31_1) =
% 10.70/2.22  |           all_31_2 & next(all_31_3) = all_31_1 & next(all_18_2) = all_31_2 &
% 10.70/2.22  |           record(all_31_1) & record(all_31_2))
% 10.70/2.22  | 
% 10.70/2.22  | GROUND_INST: instantiating (2) with all_18_6, all_29_2, all_18_8, simplifying
% 10.70/2.22  |              with (15), (29) gives:
% 10.70/2.22  |   (33)  all_29_2 = all_18_6
% 10.70/2.22  | 
% 10.70/2.22  | GROUND_INST: instantiating (2) with all_29_2, all_31_3, all_18_8, simplifying
% 10.70/2.22  |              with (29), (31) gives:
% 10.70/2.22  |   (34)  all_31_3 = all_29_2
% 10.70/2.22  | 
% 10.70/2.22  | GROUND_INST: instantiating (2) with all_27_0, all_31_3, all_18_8, simplifying
% 10.70/2.22  |              with (27), (31) gives:
% 10.70/2.22  |   (35)  all_31_3 = all_27_0
% 10.70/2.22  | 
% 10.70/2.22  | COMBINE_EQS: (34), (35) imply:
% 10.70/2.22  |   (36)  all_29_2 = all_27_0
% 10.70/2.22  | 
% 10.70/2.22  | SIMP: (36) implies:
% 10.70/2.22  |   (37)  all_29_2 = all_27_0
% 10.70/2.22  | 
% 10.70/2.22  | COMBINE_EQS: (33), (37) imply:
% 10.70/2.22  |   (38)  all_27_0 = all_18_6
% 10.70/2.22  | 
% 10.70/2.22  | SIMP: (38) implies:
% 10.70/2.22  |   (39)  all_27_0 = all_18_6
% 10.70/2.22  | 
% 10.70/2.22  | COMBINE_EQS: (35), (39) imply:
% 10.70/2.22  |   (40)  all_31_3 = all_18_6
% 10.70/2.22  | 
% 10.70/2.22  | REDUCE: (26), (39) imply:
% 10.70/2.22  |   (41)  length(all_18_6) = $sum(all_18_0, -1)
% 10.70/2.22  | 
% 10.70/2.22  | REDUCE: (25), (39) imply:
% 10.70/2.22  |   (42)  record(all_18_6)
% 10.70/2.22  | 
% 10.70/2.22  | BETA: splitting (21) gives:
% 10.70/2.22  | 
% 10.70/2.22  | Case 1:
% 10.70/2.22  | | 
% 10.70/2.22  | |   (43)  isrecord(all_18_2)
% 10.70/2.22  | | 
% 10.70/2.22  | | BETA: splitting (32) gives:
% 10.70/2.22  | | 
% 10.70/2.22  | | Case 1:
% 10.70/2.22  | | | 
% 10.70/2.22  | | |   (44)   ~ isrecord(all_31_3)
% 10.70/2.22  | | | 
% 10.70/2.22  | | | REDUCE: (40), (44) imply:
% 10.70/2.22  | | |   (45)   ~ isrecord(all_18_6)
% 10.70/2.22  | | | 
% 10.70/2.22  | | | PRED_UNIFY: (8), (45) imply:
% 10.70/2.22  | | |   (46)  $false
% 10.70/2.23  | | | 
% 10.70/2.23  | | | CLOSE: (46) is inconsistent.
% 10.70/2.23  | | | 
% 10.70/2.23  | | Case 2:
% 10.70/2.23  | | | 
% 10.70/2.23  | | |   (47)  isrecord(all_31_3)
% 10.70/2.23  | | |   (48)  all_31_0 = all_31_2 & split2(all_31_1) = all_31_2 & next(all_31_3)
% 10.70/2.23  | | |         = all_31_1 & next(all_18_2) = all_31_2 & record(all_31_1) &
% 10.70/2.23  | | |         record(all_31_2)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | ALPHA: (48) implies:
% 10.70/2.23  | | |   (49)  next(all_18_2) = all_31_2
% 10.70/2.23  | | |   (50)  next(all_31_3) = all_31_1
% 10.70/2.23  | | |   (51)  split2(all_31_1) = all_31_2
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (40), (50) imply:
% 10.70/2.23  | | |   (52)  next(all_18_6) = all_31_1
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (2) with all_18_7, all_31_1, all_18_6,
% 10.70/2.23  | | |              simplifying with (16), (52) gives:
% 10.70/2.23  | | |   (53)  all_31_1 = all_18_7
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (51), (53) imply:
% 10.70/2.23  | | |   (54)  split2(all_18_7) = all_31_2
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (3) with all_18_5, all_31_2, all_18_7,
% 10.70/2.23  | | |              simplifying with (18), (54) gives:
% 10.70/2.23  | | |   (55)  all_31_2 = all_18_5
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (49), (55) imply:
% 10.70/2.23  | | |   (56)  next(all_18_2) = all_18_5
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (ax3) with all_18_2, all_18_1, simplifying with
% 10.70/2.23  | | |              (10), (14), (43) gives:
% 10.70/2.23  | | |   (57)   ? [v0: record] : (next(all_18_2) = v0 & length(v0) =
% 10.70/2.23  | | |           $sum(all_18_1, -1) & record(v0))
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (ax3) with all_18_6, $sum(all_18_0, -1),
% 10.70/2.23  | | |              simplifying with (8), (41), (42) gives:
% 10.70/2.23  | | |   (58)   ? [v0: record] : (next(all_18_6) = v0 & length(v0) =
% 10.70/2.23  | | |           $sum(all_18_0, -2) & record(v0))
% 10.70/2.23  | | | 
% 10.70/2.23  | | | DELTA: instantiating (57) with fresh symbol all_64_0 gives:
% 10.70/2.23  | | |   (59)  next(all_18_2) = all_64_0 & length(all_64_0) = $sum(all_18_1, -1)
% 10.70/2.23  | | |         & record(all_64_0)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | ALPHA: (59) implies:
% 10.70/2.23  | | |   (60)  length(all_64_0) = $sum(all_18_1, -1)
% 10.70/2.23  | | |   (61)  next(all_18_2) = all_64_0
% 10.70/2.23  | | | 
% 10.70/2.23  | | | DELTA: instantiating (58) with fresh symbol all_66_0 gives:
% 10.70/2.23  | | |   (62)  next(all_18_6) = all_66_0 & length(all_66_0) = $sum(all_18_0, -2)
% 10.70/2.23  | | |         & record(all_66_0)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | ALPHA: (62) implies:
% 10.70/2.23  | | |   (63)  length(all_66_0) = $sum(all_18_0, -2)
% 10.70/2.23  | | |   (64)  next(all_18_6) = all_66_0
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (2) with all_18_7, all_66_0, all_18_6,
% 10.70/2.23  | | |              simplifying with (16), (64) gives:
% 10.70/2.23  | | |   (65)  all_66_0 = all_18_7
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (2) with all_18_5, all_64_0, all_18_2,
% 10.70/2.23  | | |              simplifying with (56), (61) gives:
% 10.70/2.23  | | |   (66)  all_64_0 = all_18_5
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (63), (65) imply:
% 10.70/2.23  | | |   (67)  length(all_18_7) = $sum(all_18_0, -2)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (60), (66) imply:
% 10.70/2.23  | | |   (68)  length(all_18_5) = $sum(all_18_1, -1)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (1) with all_18_3, $sum(all_18_0, -2),
% 10.70/2.23  | | |              all_18_7, simplifying with (12), (67) gives:
% 10.70/2.23  | | |   (69)  $difference(all_18_0, all_18_3) = 2
% 10.70/2.23  | | | 
% 10.70/2.23  | | | GROUND_INST: instantiating (1) with all_18_4, $sum(all_18_1, -1),
% 10.70/2.23  | | |              all_18_5, simplifying with (13), (68) gives:
% 10.70/2.23  | | |   (70)  $difference(all_18_1, all_18_4) = 1
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (6), (69), (70) imply:
% 10.70/2.23  | | |   (71)   ~ ($difference(all_18_3, $product(2, all_18_4)) = 1)
% 10.70/2.23  | | | 
% 10.70/2.23  | | | REDUCE: (5), (69), (70) imply:
% 10.70/2.24  | | |   (72)   ~ (all_18_3 = $product(2, all_18_4))
% 10.70/2.24  | | | 
% 10.70/2.24  | | | BETA: splitting (19) gives:
% 10.70/2.24  | | | 
% 10.70/2.24  | | | Case 1:
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | |   (73)  all_18_3 = $product(2, all_18_4)
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | | REDUCE: (72), (73) imply:
% 10.70/2.24  | | | |   (74)  $false
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | | CLOSE: (74) is inconsistent.
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | Case 2:
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | |   (75)  $difference(all_18_3, $product(2, all_18_4)) = 1
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | | REDUCE: (71), (75) imply:
% 10.70/2.24  | | | |   (76)  $false
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | | CLOSE: (76) is inconsistent.
% 10.70/2.24  | | | | 
% 10.70/2.24  | | | End of split
% 10.70/2.24  | | | 
% 10.70/2.24  | | End of split
% 10.70/2.24  | | 
% 10.70/2.24  | Case 2:
% 10.70/2.24  | | 
% 10.70/2.24  | |   (77)   ? [v0: record] : (next(all_18_8) = v0 & record(v0) &  ~
% 10.70/2.24  | |           isrecord(v0))
% 10.70/2.24  | | 
% 10.70/2.24  | | DELTA: instantiating (77) with fresh symbol all_41_0 gives:
% 10.70/2.24  | |   (78)  next(all_18_8) = all_41_0 & record(all_41_0) &  ~ isrecord(all_41_0)
% 10.70/2.24  | | 
% 10.70/2.24  | | ALPHA: (78) implies:
% 10.70/2.24  | |   (79)   ~ isrecord(all_41_0)
% 10.70/2.24  | |   (80)  next(all_18_8) = all_41_0
% 10.70/2.24  | | 
% 10.70/2.24  | | GROUND_INST: instantiating (2) with all_18_6, all_41_0, all_18_8,
% 10.70/2.24  | |              simplifying with (15), (80) gives:
% 10.70/2.24  | |   (81)  all_41_0 = all_18_6
% 10.70/2.24  | | 
% 10.70/2.24  | | REDUCE: (79), (81) imply:
% 10.70/2.24  | |   (82)   ~ isrecord(all_18_6)
% 10.70/2.24  | | 
% 10.70/2.24  | | PRED_UNIFY: (8), (82) imply:
% 10.70/2.24  | |   (83)  $false
% 10.70/2.24  | | 
% 10.70/2.24  | | CLOSE: (83) is inconsistent.
% 10.70/2.24  | | 
% 10.70/2.24  | End of split
% 10.70/2.24  | 
% 10.70/2.24  End of proof
% 10.70/2.24  % SZS output end Proof for theBenchmark
% 10.70/2.24  
% 10.70/2.24  1624ms
%------------------------------------------------------------------------------