TSTP Solution File: COM023+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : COM023+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 May 19 10:13:56 EDT 2023

% Result   : Theorem 3.73s 1.91s
% Output   : Refutation 4.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   49 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :  214 (   3 equ;   0 cnn)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  545 (   5   ~;   6   |; 104   &; 364   @)
%                                         (   6 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  103 (   0   ^;  87   !;  16   ?; 103   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aElement0_type,type,
    aElement0: $i > $o ).

thf(aRewritingSystem0_type,type,
    aRewritingSystem0: $i > $o ).

thf(sdtmndtplgtdt0_type,type,
    sdtmndtplgtdt0: $i > $i > $i > $o ).

thf(aReductOfIn0_type,type,
    aReductOfIn0: $i > $i > $i > $o ).

thf(sdtmndtasgtdt0_type,type,
    sdtmndtasgtdt0: $i > $i > $i > $o ).

thf(isConfluent0_type,type,
    isConfluent0: $i > $o ).

thf(isLocallyConfluent0_type,type,
    isLocallyConfluent0: $i > $o ).

thf(isTerminating0_type,type,
    isTerminating0: $i > $o ).

thf(iLess0_type,type,
    iLess0: $i > $i > $o ).

thf(aNormalFormOfIn0_type,type,
    aNormalFormOfIn0: $i > $i > $i > $o ).

thf(xR_type,type,
    xR: $i ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( iLess0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWFOrd) ).

thf(69,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B ) )
     => ! [C: $i] :
          ( ( aReductOfIn0 @ C @ A @ B )
         => ( aElement0 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).

thf(24,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B ) )
     => ! [C: $i] :
          ( ( aReductOfIn0 @ C @ A @ B )
         => ( aElement0 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C )
        & ( aElement0 @ D ) )
     => ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
          & ( sdtmndtplgtdt0 @ C @ B @ D ) )
       => ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCTrans) ).

thf(61,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C )
        & ( aElement0 @ D ) )
     => ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
          & ( sdtmndtplgtdt0 @ C @ B @ D ) )
       => ( sdtmndtplgtdt0 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C )
        & ( sdtmndtasgtdt0 @ A @ xR @ B )
        & ( sdtmndtasgtdt0 @ A @ xR @ C ) )
     => ? [D: $i] :
          ( ( aElement0 @ D )
          & ( sdtmndtasgtdt0 @ B @ xR @ D )
          & ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).

thf(85,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C )
        & ( sdtmndtasgtdt0 @ A @ xR @ B )
        & ( sdtmndtasgtdt0 @ A @ xR @ C ) )
     => ? [D: $i] :
          ( ( aElement0 @ D )
          & ( sdtmndtasgtdt0 @ B @ xR @ D )
          & ( sdtmndtasgtdt0 @ C @ xR @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( isTerminating0 @ A )
      <=> ! [B: $i,C: $i] :
            ( ( ( aElement0 @ B )
              & ( aElement0 @ C ) )
           => ( ( sdtmndtplgtdt0 @ B @ A @ C )
             => ( iLess0 @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermin) ).

thf(41,plain,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( ( isTerminating0 @ A )
         => ! [B: $i,C: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C ) )
             => ( ( sdtmndtplgtdt0 @ B @ A @ C )
               => ( iLess0 @ C @ B ) ) ) )
        & ( ! [B: $i,C: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C ) )
             => ( ( sdtmndtplgtdt0 @ B @ A @ C )
               => ( iLess0 @ C @ B ) ) )
         => ( isTerminating0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C )
        & ( aElement0 @ D ) )
     => ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
          & ( sdtmndtasgtdt0 @ C @ B @ D ) )
       => ( sdtmndtasgtdt0 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).

thf(22,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C )
        & ( aElement0 @ D ) )
     => ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
          & ( sdtmndtasgtdt0 @ C @ B @ D ) )
       => ( sdtmndtasgtdt0 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B ) )
     => ! [C: $i] :
          ( ( aNormalFormOfIn0 @ C @ A @ B )
        <=> ( ( aElement0 @ C )
            & ( sdtmndtasgtdt0 @ A @ B @ C )
            & ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNFRDef) ).

thf(54,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B ) )
     => ! [C: $i] :
          ( ( ( aNormalFormOfIn0 @ C @ A @ B )
           => ( ( aElement0 @ C )
              & ( sdtmndtasgtdt0 @ A @ B @ C )
              & ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) ) )
          & ( ( ( aElement0 @ C )
              & ( sdtmndtasgtdt0 @ A @ B @ C )
              & ~ ? [D: $i] : ( aReductOfIn0 @ D @ C @ B ) )
           => ( aNormalFormOfIn0 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(17,axiom,
    aRewritingSystem0 @ xR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).

thf(81,plain,
    aRewritingSystem0 @ xR,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtmndtplgtdt0 @ A @ B @ C )
      <=> ( ( aReductOfIn0 @ C @ A @ B )
          | ? [D: $i] :
              ( ( aElement0 @ D )
              & ( aReductOfIn0 @ D @ A @ B )
              & ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).

thf(63,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C ) )
     => ( ( ( sdtmndtplgtdt0 @ A @ B @ C )
         => ( ( aReductOfIn0 @ C @ A @ B )
            | ? [D: $i] :
                ( ( aElement0 @ D )
                & ( aReductOfIn0 @ D @ A @ B )
                & ( sdtmndtplgtdt0 @ D @ B @ C ) ) ) )
        & ( ( ( aReductOfIn0 @ C @ A @ B )
            | ? [D: $i] :
                ( ( aElement0 @ D )
                & ( aReductOfIn0 @ D @ A @ B )
                & ( sdtmndtplgtdt0 @ D @ B @ C ) ) )
         => ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ( aRewritingSystem0 @ A )
        & ( isTerminating0 @ A ) )
     => ! [B: $i] :
          ( ( aElement0 @ B )
         => ? [C: $i] : ( aNormalFormOfIn0 @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).

thf(26,plain,
    ! [A: $i] :
      ( ( ( aRewritingSystem0 @ A )
        & ( isTerminating0 @ A ) )
     => ! [B: $i] :
          ( ( aElement0 @ B )
         => ? [C: $i] : ( aNormalFormOfIn0 @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(18,axiom,
    ( ( isLocallyConfluent0 @ xR )
    & ( isTerminating0 @ xR ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).

thf(82,plain,
    ( ( isLocallyConfluent0 @ xR )
    & ( isTerminating0 @ xR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( isLocallyConfluent0 @ A )
      <=> ! [B: $i,C: $i,D: $i] :
            ( ( ( aElement0 @ B )
              & ( aElement0 @ C )
              & ( aElement0 @ D )
              & ( aReductOfIn0 @ C @ B @ A )
              & ( aReductOfIn0 @ D @ B @ A ) )
           => ? [E: $i] :
                ( ( aElement0 @ E )
                & ( sdtmndtasgtdt0 @ C @ A @ E )
                & ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWCRDef) ).

thf(30,plain,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( ( isLocallyConfluent0 @ A )
         => ! [B: $i,C: $i,D: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C )
                & ( aElement0 @ D )
                & ( aReductOfIn0 @ C @ B @ A )
                & ( aReductOfIn0 @ D @ B @ A ) )
             => ? [E: $i] :
                  ( ( aElement0 @ E )
                  & ( sdtmndtasgtdt0 @ C @ A @ E )
                  & ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) )
        & ( ! [B: $i,C: $i,D: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C )
                & ( aElement0 @ D )
                & ( aReductOfIn0 @ C @ B @ A )
                & ( aReductOfIn0 @ D @ B @ A ) )
             => ? [E: $i] :
                  ( ( aElement0 @ E )
                  & ( sdtmndtasgtdt0 @ C @ A @ E )
                  & ( sdtmndtasgtdt0 @ D @ A @ E ) ) )
         => ( isLocallyConfluent0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtmndtasgtdt0 @ A @ B @ C )
      <=> ( ( A = C )
          | ( sdtmndtplgtdt0 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).

thf(47,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C ) )
     => ( ( ( sdtmndtasgtdt0 @ A @ B @ C )
         => ( ( A = C )
            | ( sdtmndtplgtdt0 @ A @ B @ C ) ) )
        & ( ( ( A = C )
            | ( sdtmndtplgtdt0 @ A @ B @ C ) )
         => ( sdtmndtasgtdt0 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,conjecture,
    isConfluent0 @ xR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( isConfluent0 @ xR ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(20,plain,
    ~ ( isConfluent0 @ xR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aRewritingSystem0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtmndtplgtdt0 @ A @ B @ C )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCbr) ).

thf(29,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).

thf(28,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( isConfluent0 @ A )
      <=> ! [B: $i,C: $i,D: $i] :
            ( ( ( aElement0 @ B )
              & ( aElement0 @ C )
              & ( aElement0 @ D )
              & ( sdtmndtasgtdt0 @ B @ A @ C )
              & ( sdtmndtasgtdt0 @ B @ A @ D ) )
           => ? [E: $i] :
                ( ( aElement0 @ E )
                & ( sdtmndtasgtdt0 @ C @ A @ E )
                & ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCRDef) ).

thf(70,plain,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => ( ( ( isConfluent0 @ A )
         => ! [B: $i,C: $i,D: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C )
                & ( aElement0 @ D )
                & ( sdtmndtasgtdt0 @ B @ A @ C )
                & ( sdtmndtasgtdt0 @ B @ A @ D ) )
             => ? [E: $i] :
                  ( ( aElement0 @ E )
                  & ( sdtmndtasgtdt0 @ C @ A @ E )
                  & ( sdtmndtasgtdt0 @ D @ A @ E ) ) ) )
        & ( ! [B: $i,C: $i,D: $i] :
              ( ( ( aElement0 @ B )
                & ( aElement0 @ C )
                & ( aElement0 @ D )
                & ( sdtmndtasgtdt0 @ B @ A @ C )
                & ( sdtmndtasgtdt0 @ B @ A @ D ) )
             => ? [E: $i] :
                  ( ( aElement0 @ E )
                  & ( sdtmndtasgtdt0 @ C @ A @ E )
                  & ( sdtmndtasgtdt0 @ D @ A @ E ) ) )
         => ( isConfluent0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( aRewritingSystem0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mRelSort) ).

thf(21,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(89,plain,
    $false,
    inference(cvc4,[status(thm)],[69,24,61,85,41,22,54,81,63,26,82,30,47,20,29,28,70,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COM023+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May 19 03:07:54 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.93/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.03  % [INFO] 	 Parsing done (140ms). 
% 1.25/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.27  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.28  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.29  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.29  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.29  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.30  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.88/1.31  % [INFO] 	 Found a conjecture and 17 axioms. Running axiom selection ... 
% 2.13/1.35  % [INFO] 	 Axiom selection finished. Selected 17 axioms (removed 0 axioms). 
% 2.13/1.35  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.13/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.13/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.13/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.13/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.13/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.23/1.37  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.23/1.37  % [INFO] 	 Type checking passed. 
% 2.23/1.38  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.73/1.91  % External prover 'cvc4' found a proof!
% 3.73/1.91  % [INFO] 	 Killing All external provers ... 
% 3.73/1.91  % Time passed: 1381ms (effective reasoning time: 865ms)
% 3.73/1.91  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.73/1.91  % Axioms used in derivation (17): mTermNF, mTermin, m__656_01, mWCRDef, mTCTrans, mNFRDef, mReduct, m__715, mTCDef, mRelSort, mTCRDef, mWFOrd, m__656, mTCRTrans, mTCbr, mElmSort, mCRDef
% 3.73/1.91  % No. of inferences in proof: 38
% 3.73/1.91  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1381 ms resp. 865 ms w/o parsing
% 4.11/1.95  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.11/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------