TSTP Solution File: SEU165+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:42:58 EDT 2023

% Result   : Theorem 4.53s 1.36s
% Output   : Proof 6.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n012.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 : Wed Aug 23 22:05:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61  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 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 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 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 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/0.97  Prover 4: Preprocessing ...
% 1.97/0.98  Prover 1: Preprocessing ...
% 2.38/1.02  Prover 2: Preprocessing ...
% 2.38/1.02  Prover 5: Preprocessing ...
% 2.38/1.02  Prover 3: Preprocessing ...
% 2.38/1.02  Prover 6: Preprocessing ...
% 2.38/1.02  Prover 0: Preprocessing ...
% 3.72/1.21  Prover 6: Constructing countermodel ...
% 3.72/1.21  Prover 4: Constructing countermodel ...
% 3.72/1.22  Prover 3: Constructing countermodel ...
% 3.72/1.22  Prover 5: Proving ...
% 3.72/1.22  Prover 1: Constructing countermodel ...
% 3.72/1.23  Prover 2: Proving ...
% 3.72/1.24  Prover 0: Proving ...
% 4.53/1.36  Prover 3: proved (728ms)
% 4.53/1.36  
% 4.53/1.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.53/1.36  
% 4.53/1.36  Prover 0: stopped
% 4.53/1.36  Prover 5: stopped
% 4.53/1.36  Prover 2: stopped
% 4.53/1.36  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.53/1.36  Prover 6: stopped
% 4.53/1.37  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.53/1.37  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.53/1.37  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.53/1.37  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.53/1.38  Prover 11: Preprocessing ...
% 4.53/1.40  Prover 13: Preprocessing ...
% 4.53/1.40  Prover 10: Preprocessing ...
% 4.53/1.41  Prover 7: Preprocessing ...
% 4.53/1.41  Prover 8: Preprocessing ...
% 4.53/1.45  Prover 10: Constructing countermodel ...
% 4.53/1.46  Prover 13: Warning: ignoring some quantifiers
% 4.53/1.47  Prover 13: Constructing countermodel ...
% 4.53/1.47  Prover 7: Constructing countermodel ...
% 5.32/1.48  Prover 1: Found proof (size 32)
% 5.32/1.48  Prover 1: proved (858ms)
% 5.32/1.48  Prover 13: stopped
% 5.32/1.48  Prover 4: stopped
% 5.32/1.48  Prover 10: stopped
% 5.32/1.48  Prover 7: stopped
% 5.32/1.49  Prover 8: Warning: ignoring some quantifiers
% 5.32/1.49  Prover 8: Constructing countermodel ...
% 5.32/1.49  Prover 8: stopped
% 5.32/1.50  Prover 11: Constructing countermodel ...
% 5.32/1.51  Prover 11: stopped
% 5.32/1.51  
% 5.32/1.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.32/1.51  
% 5.32/1.51  % SZS output start Proof for theBenchmark
% 5.32/1.52  Assumptions after simplification:
% 5.32/1.52  ---------------------------------
% 5.32/1.52  
% 5.32/1.52    (l55_zfmisc_1)
% 5.32/1.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 5.32/1.55      $i] :  ! [v6: int] : (v6 = 0 |  ~ (cartesian_product2(v2, v3) = v5) |  ~
% 5.32/1.55      (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = v6) |  ~ $i(v3) |  ~ $i(v2) |
% 5.32/1.55       ~ $i(v1) |  ~ $i(v0) |  ? [v7: any] :  ? [v8: any] : (in(v1, v3) = v8 &
% 5.32/1.55        in(v0, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0: $i] :  ! [v1:
% 5.32/1.55      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~
% 5.32/1.55      (cartesian_product2(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~
% 5.32/1.55      (in(v4, v5) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (in(v1,
% 5.32/1.55          v3) = 0 & in(v0, v2) = 0))
% 5.32/1.55  
% 5.32/1.55    (t106_zfmisc_1)
% 5.32/1.55     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 5.32/1.56      $i] :  ? [v6: any] :  ? [v7: any] :  ? [v8: any] : (cartesian_product2(v2,
% 5.32/1.56        v3) = v5 & ordered_pair(v0, v1) = v4 & in(v4, v5) = v6 & in(v1, v3) = v8 &
% 5.32/1.56      in(v0, v2) = v7 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8
% 5.32/1.56          = 0 & v7 = 0 &  ~ (v6 = 0)) | (v6 = 0 & ( ~ (v8 = 0) |  ~ (v7 = 0)))))
% 5.32/1.56  
% 5.32/1.56    (function-axioms)
% 5.32/1.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 5.32/1.56      (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) & 
% 5.32/1.56    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 5.32/1.56      (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0:
% 5.32/1.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 5.32/1.56    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0: $i] :  !
% 5.32/1.56    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unordered_pair(v3, v2) =
% 5.32/1.56        v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 5.32/1.56    [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  !
% 5.32/1.56    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0
% 5.32/1.56      |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 5.32/1.56  
% 5.32/1.56  Further assumptions not needed in the proof:
% 5.32/1.56  --------------------------------------------
% 5.32/1.56  antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 5.32/1.56  rc1_xboole_0, rc2_xboole_0
% 5.32/1.56  
% 5.32/1.56  Those formulas are unsatisfiable:
% 5.32/1.56  ---------------------------------
% 5.32/1.56  
% 5.32/1.56  Begin of proof
% 5.32/1.56  | 
% 5.32/1.56  | ALPHA: (l55_zfmisc_1) implies:
% 5.32/1.57  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 5.32/1.57  |        ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) |  ~
% 5.32/1.57  |          (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = 0) |  ~ $i(v3) |  ~
% 5.32/1.57  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 6.12/1.57  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 6.12/1.57  |        ! [v5: $i] :  ! [v6: int] : (v6 = 0 |  ~ (cartesian_product2(v2, v3) =
% 6.12/1.57  |            v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = v6) |  ~
% 6.12/1.57  |          $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: any] :  ? [v8:
% 6.12/1.57  |            any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 =
% 6.12/1.57  |                0))))
% 6.12/1.57  | 
% 6.12/1.57  | ALPHA: (function-axioms) implies:
% 6.12/1.57  |   (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.12/1.57  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.12/1.57  | 
% 6.12/1.57  | DELTA: instantiating (t106_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 6.12/1.57  |        all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8
% 6.12/1.57  |        gives:
% 6.12/1.58  |   (4)  cartesian_product2(all_12_6, all_12_5) = all_12_3 &
% 6.12/1.58  |        ordered_pair(all_12_8, all_12_7) = all_12_4 & in(all_12_4, all_12_3) =
% 6.12/1.58  |        all_12_2 & in(all_12_7, all_12_5) = all_12_0 & in(all_12_8, all_12_6) =
% 6.12/1.58  |        all_12_1 & $i(all_12_3) & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) &
% 6.12/1.58  |        $i(all_12_7) & $i(all_12_8) & ((all_12_0 = 0 & all_12_1 = 0 &  ~
% 6.12/1.58  |            (all_12_2 = 0)) | (all_12_2 = 0 & ( ~ (all_12_0 = 0) |  ~ (all_12_1
% 6.12/1.58  |                = 0))))
% 6.12/1.58  | 
% 6.12/1.58  | ALPHA: (4) implies:
% 6.12/1.58  |   (5)  $i(all_12_8)
% 6.12/1.58  |   (6)  $i(all_12_7)
% 6.12/1.58  |   (7)  $i(all_12_6)
% 6.12/1.58  |   (8)  $i(all_12_5)
% 6.12/1.58  |   (9)  in(all_12_8, all_12_6) = all_12_1
% 6.12/1.58  |   (10)  in(all_12_7, all_12_5) = all_12_0
% 6.12/1.58  |   (11)  in(all_12_4, all_12_3) = all_12_2
% 6.12/1.58  |   (12)  ordered_pair(all_12_8, all_12_7) = all_12_4
% 6.12/1.58  |   (13)  cartesian_product2(all_12_6, all_12_5) = all_12_3
% 6.12/1.58  |   (14)  (all_12_0 = 0 & all_12_1 = 0 &  ~ (all_12_2 = 0)) | (all_12_2 = 0 & (
% 6.12/1.58  |             ~ (all_12_0 = 0) |  ~ (all_12_1 = 0)))
% 6.12/1.58  | 
% 6.12/1.58  | GROUND_INST: instantiating (2) with all_12_8, all_12_7, all_12_6, all_12_5,
% 6.12/1.58  |              all_12_4, all_12_3, all_12_2, simplifying with (5), (6), (7),
% 6.12/1.58  |              (8), (11), (12), (13) gives:
% 6.12/1.58  |   (15)  all_12_2 = 0 |  ? [v0: any] :  ? [v1: any] : (in(all_12_7, all_12_5) =
% 6.12/1.58  |           v1 & in(all_12_8, all_12_6) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.12/1.58  | 
% 6.12/1.58  | BETA: splitting (14) gives:
% 6.12/1.58  | 
% 6.12/1.58  | Case 1:
% 6.12/1.58  | | 
% 6.12/1.58  | |   (16)  all_12_0 = 0 & all_12_1 = 0 &  ~ (all_12_2 = 0)
% 6.12/1.58  | | 
% 6.12/1.58  | | ALPHA: (16) implies:
% 6.12/1.58  | |   (17)  all_12_1 = 0
% 6.12/1.58  | |   (18)  all_12_0 = 0
% 6.12/1.58  | |   (19)   ~ (all_12_2 = 0)
% 6.12/1.58  | | 
% 6.12/1.58  | | REDUCE: (10), (18) imply:
% 6.12/1.59  | |   (20)  in(all_12_7, all_12_5) = 0
% 6.12/1.59  | | 
% 6.12/1.59  | | REDUCE: (9), (17) imply:
% 6.12/1.59  | |   (21)  in(all_12_8, all_12_6) = 0
% 6.12/1.59  | | 
% 6.12/1.59  | | BETA: splitting (15) gives:
% 6.12/1.59  | | 
% 6.12/1.59  | | Case 1:
% 6.12/1.59  | | | 
% 6.12/1.59  | | |   (22)  all_12_2 = 0
% 6.12/1.59  | | | 
% 6.12/1.59  | | | REDUCE: (19), (22) imply:
% 6.12/1.59  | | |   (23)  $false
% 6.12/1.59  | | | 
% 6.12/1.59  | | | CLOSE: (23) is inconsistent.
% 6.12/1.59  | | | 
% 6.12/1.59  | | Case 2:
% 6.12/1.59  | | | 
% 6.12/1.59  | | |   (24)   ? [v0: any] :  ? [v1: any] : (in(all_12_7, all_12_5) = v1 &
% 6.12/1.59  | | |           in(all_12_8, all_12_6) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.12/1.59  | | | 
% 6.12/1.59  | | | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1 gives:
% 6.12/1.59  | | |   (25)  in(all_12_7, all_12_5) = all_32_0 & in(all_12_8, all_12_6) =
% 6.12/1.59  | | |         all_32_1 & ( ~ (all_32_0 = 0) |  ~ (all_32_1 = 0))
% 6.12/1.59  | | | 
% 6.12/1.59  | | | ALPHA: (25) implies:
% 6.12/1.59  | | |   (26)  in(all_12_8, all_12_6) = all_32_1
% 6.12/1.59  | | |   (27)  in(all_12_7, all_12_5) = all_32_0
% 6.12/1.59  | | |   (28)   ~ (all_32_0 = 0) |  ~ (all_32_1 = 0)
% 6.12/1.59  | | | 
% 6.12/1.59  | | | GROUND_INST: instantiating (3) with 0, all_32_1, all_12_6, all_12_8,
% 6.12/1.59  | | |              simplifying with (21), (26) gives:
% 6.12/1.59  | | |   (29)  all_32_1 = 0
% 6.12/1.59  | | | 
% 6.12/1.59  | | | GROUND_INST: instantiating (3) with 0, all_32_0, all_12_5, all_12_7,
% 6.12/1.59  | | |              simplifying with (20), (27) gives:
% 6.12/1.59  | | |   (30)  all_32_0 = 0
% 6.12/1.59  | | | 
% 6.12/1.59  | | | BETA: splitting (28) gives:
% 6.12/1.59  | | | 
% 6.12/1.59  | | | Case 1:
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | |   (31)   ~ (all_32_0 = 0)
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | | REDUCE: (30), (31) imply:
% 6.12/1.59  | | | |   (32)  $false
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | | CLOSE: (32) is inconsistent.
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | Case 2:
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | |   (33)   ~ (all_32_1 = 0)
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | | REDUCE: (29), (33) imply:
% 6.12/1.59  | | | |   (34)  $false
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | | CLOSE: (34) is inconsistent.
% 6.12/1.59  | | | | 
% 6.12/1.59  | | | End of split
% 6.12/1.59  | | | 
% 6.12/1.59  | | End of split
% 6.12/1.59  | | 
% 6.12/1.59  | Case 2:
% 6.12/1.59  | | 
% 6.12/1.59  | |   (35)  all_12_2 = 0 & ( ~ (all_12_0 = 0) |  ~ (all_12_1 = 0))
% 6.12/1.59  | | 
% 6.12/1.59  | | ALPHA: (35) implies:
% 6.12/1.59  | |   (36)  all_12_2 = 0
% 6.12/1.59  | |   (37)   ~ (all_12_0 = 0) |  ~ (all_12_1 = 0)
% 6.12/1.59  | | 
% 6.12/1.59  | | REDUCE: (11), (36) imply:
% 6.12/1.59  | |   (38)  in(all_12_4, all_12_3) = 0
% 6.12/1.59  | | 
% 6.12/1.60  | | GROUND_INST: instantiating (1) with all_12_8, all_12_7, all_12_6, all_12_5,
% 6.12/1.60  | |              all_12_4, all_12_3, simplifying with (5), (6), (7), (8), (12),
% 6.12/1.60  | |              (13), (38) gives:
% 6.12/1.60  | |   (39)  in(all_12_7, all_12_5) = 0 & in(all_12_8, all_12_6) = 0
% 6.12/1.60  | | 
% 6.12/1.60  | | ALPHA: (39) implies:
% 6.12/1.60  | |   (40)  in(all_12_8, all_12_6) = 0
% 6.12/1.60  | |   (41)  in(all_12_7, all_12_5) = 0
% 6.12/1.60  | | 
% 6.12/1.60  | | GROUND_INST: instantiating (3) with all_12_1, 0, all_12_6, all_12_8,
% 6.12/1.60  | |              simplifying with (9), (40) gives:
% 6.12/1.60  | |   (42)  all_12_1 = 0
% 6.12/1.60  | | 
% 6.12/1.60  | | GROUND_INST: instantiating (3) with all_12_0, 0, all_12_5, all_12_7,
% 6.12/1.60  | |              simplifying with (10), (41) gives:
% 6.12/1.60  | |   (43)  all_12_0 = 0
% 6.12/1.60  | | 
% 6.12/1.60  | | BETA: splitting (37) gives:
% 6.12/1.60  | | 
% 6.12/1.60  | | Case 1:
% 6.12/1.60  | | | 
% 6.12/1.60  | | |   (44)   ~ (all_12_0 = 0)
% 6.12/1.60  | | | 
% 6.12/1.60  | | | REDUCE: (43), (44) imply:
% 6.12/1.60  | | |   (45)  $false
% 6.12/1.60  | | | 
% 6.12/1.60  | | | CLOSE: (45) is inconsistent.
% 6.12/1.60  | | | 
% 6.12/1.60  | | Case 2:
% 6.12/1.60  | | | 
% 6.12/1.60  | | |   (46)   ~ (all_12_1 = 0)
% 6.12/1.60  | | | 
% 6.12/1.60  | | | REDUCE: (42), (46) imply:
% 6.12/1.60  | | |   (47)  $false
% 6.12/1.60  | | | 
% 6.12/1.60  | | | CLOSE: (47) is inconsistent.
% 6.12/1.60  | | | 
% 6.12/1.60  | | End of split
% 6.12/1.60  | | 
% 6.12/1.60  | End of split
% 6.12/1.60  | 
% 6.12/1.60  End of proof
% 6.12/1.60  % SZS output end Proof for theBenchmark
% 6.12/1.60  
% 6.12/1.60  996ms
%------------------------------------------------------------------------------