TSTP Solution File: SEU997^5 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU997^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 : Tue May 21 03:40:37 EDT 2024

% Result   : Theorem 3.54s 2.12s
% Output   : Refutation 3.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    5 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :   64 (  63 equ;   0 cnn)
%            Maximal formula atoms :   21 (  16 avg)
%            Number of connectives :  290 (   2   ~;   0   |;  54   &; 228   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  18 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0 usr;   1 con; 0-2 aty)
%            Number of variables   :  105 (   0   ^ 102   !;   3   ?; 105   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(1,conjecture,
    ! [A: a > a > a,B: a > a > a,C: a,D: a] :
      ( ( ! [E: a] :
            ( ( A @ E @ E )
            = E )
        & ! [E: a] :
            ( ( B @ E @ E )
            = E )
        & ! [E: a,F: a,G: a] :
            ( ( A @ ( A @ E @ F ) @ G )
            = ( A @ E @ ( A @ F @ G ) ) )
        & ! [E: a,F: a,G: a] :
            ( ( B @ ( B @ E @ F ) @ G )
            = ( B @ E @ ( B @ F @ G ) ) )
        & ! [E: a,F: a] :
            ( ( A @ E @ F )
            = ( A @ F @ E ) )
        & ! [E: a,F: a] :
            ( ( B @ E @ F )
            = ( B @ F @ E ) )
        & ! [E: a,F: a] :
            ( ( A @ ( B @ E @ F ) @ F )
            = F )
        & ! [E: a,F: a] :
            ( ( B @ ( A @ E @ F ) @ F )
            = F )
        & ! [E: a,F: a,G: a] :
            ( ( B @ E @ ( A @ F @ G ) )
            = ( A @ ( B @ E @ F ) @ ( B @ E @ G ) ) )
        & ! [E: a,F: a,G: a] :
            ( ( A @ E @ ( B @ F @ G ) )
            = ( B @ ( A @ E @ F ) @ ( A @ E @ G ) ) )
        & ! [E: a] :
            ( ( B @ C @ E )
            = E )
        & ! [E: a] :
            ( ( A @ C @ E )
            = C )
        & ! [E: a] :
            ( ( B @ D @ E )
            = D )
        & ! [E: a] :
            ( ( A @ D @ E )
            = E )
        & ! [E: a] :
          ? [F: a] :
            ( ( ( A @ E @ F )
              = C )
            & ( ( B @ E @ F )
              = D ) ) )
     => ! [E: a,F: a,G: a] :
          ( ( ( ( A @ E @ F )
              = C )
            & ( ( B @ E @ F )
              = D )
            & ( ( A @ E @ G )
              = C )
            & ( ( B @ E @ G )
              = D ) )
         => ( F = G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > a > a,B: a > a > a,C: a,D: a] :
        ( ( ! [E: a] :
              ( ( A @ E @ E )
              = E )
          & ! [E: a] :
              ( ( B @ E @ E )
              = E )
          & ! [E: a,F: a,G: a] :
              ( ( A @ ( A @ E @ F ) @ G )
              = ( A @ E @ ( A @ F @ G ) ) )
          & ! [E: a,F: a,G: a] :
              ( ( B @ ( B @ E @ F ) @ G )
              = ( B @ E @ ( B @ F @ G ) ) )
          & ! [E: a,F: a] :
              ( ( A @ E @ F )
              = ( A @ F @ E ) )
          & ! [E: a,F: a] :
              ( ( B @ E @ F )
              = ( B @ F @ E ) )
          & ! [E: a,F: a] :
              ( ( A @ ( B @ E @ F ) @ F )
              = F )
          & ! [E: a,F: a] :
              ( ( B @ ( A @ E @ F ) @ F )
              = F )
          & ! [E: a,F: a,G: a] :
              ( ( B @ E @ ( A @ F @ G ) )
              = ( A @ ( B @ E @ F ) @ ( B @ E @ G ) ) )
          & ! [E: a,F: a,G: a] :
              ( ( A @ E @ ( B @ F @ G ) )
              = ( B @ ( A @ E @ F ) @ ( A @ E @ G ) ) )
          & ! [E: a] :
              ( ( B @ C @ E )
              = E )
          & ! [E: a] :
              ( ( A @ C @ E )
              = C )
          & ! [E: a] :
              ( ( B @ D @ E )
              = D )
          & ! [E: a] :
              ( ( A @ D @ E )
              = E )
          & ! [E: a] :
            ? [F: a] :
              ( ( ( A @ E @ F )
                = C )
              & ( ( B @ E @ F )
                = D ) ) )
       => ! [E: a,F: a,G: a] :
            ( ( ( ( A @ E @ F )
                = C )
              & ( ( B @ E @ F )
                = D )
              & ( ( A @ E @ G )
                = C )
              & ( ( B @ E @ G )
                = D ) )
           => ( F = G ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > a > a,B: a > a > a,C: a,D: a] :
        ( ( ! [E: a] :
              ( ( A @ E @ E )
              = E )
          & ! [E: a] :
              ( ( B @ E @ E )
              = E )
          & ! [E: a,F: a,G: a] :
              ( ( A @ ( A @ E @ F ) @ G )
              = ( A @ E @ ( A @ F @ G ) ) )
          & ! [E: a,F: a,G: a] :
              ( ( B @ ( B @ E @ F ) @ G )
              = ( B @ E @ ( B @ F @ G ) ) )
          & ! [E: a,F: a] :
              ( ( A @ E @ F )
              = ( A @ F @ E ) )
          & ! [E: a,F: a] :
              ( ( B @ E @ F )
              = ( B @ F @ E ) )
          & ! [E: a,F: a] :
              ( ( A @ ( B @ E @ F ) @ F )
              = F )
          & ! [E: a,F: a] :
              ( ( B @ ( A @ E @ F ) @ F )
              = F )
          & ! [E: a,F: a,G: a] :
              ( ( B @ E @ ( A @ F @ G ) )
              = ( A @ ( B @ E @ F ) @ ( B @ E @ G ) ) )
          & ! [E: a,F: a,G: a] :
              ( ( A @ E @ ( B @ F @ G ) )
              = ( B @ ( A @ E @ F ) @ ( A @ E @ G ) ) )
          & ! [E: a] :
              ( ( B @ C @ E )
              = E )
          & ! [E: a] :
              ( ( A @ C @ E )
              = C )
          & ! [E: a] :
              ( ( B @ D @ E )
              = D )
          & ! [E: a] :
              ( ( A @ D @ E )
              = E )
          & ! [E: a] :
            ? [F: a] :
              ( ( ( A @ E @ F )
                = C )
              & ( ( B @ E @ F )
                = D ) ) )
       => ! [E: a,F: a,G: a] :
            ( ( ( ( A @ E @ F )
                = C )
              & ( ( B @ E @ F )
                = D )
              & ( ( A @ E @ G )
                = C )
              & ( ( B @ E @ G )
                = D ) )
           => ( F = G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(61,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU997^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n008.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 18:12:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.04/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.03  % [INFO] 	 Parsing done (122ms). 
% 1.31/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.75/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.18/1.43  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.18/1.43  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.18/1.44  % [INFO] 	 Type checking passed. 
% 2.18/1.45  % [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 ... 
% 3.54/2.12  % External prover 'e' found a proof!
% 3.54/2.12  % [INFO] 	 Killing All external provers ... 
% 3.54/2.12  % Time passed: 1566ms (effective reasoning time: 1072ms)
% 3.54/2.12  % 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)>
% 3.54/2.12  % Axioms used in derivation (0): 
% 3.54/2.12  % No. of inferences in proof: 4
% 3.54/2.12  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1566 ms resp. 1072 ms w/o parsing
% 3.94/2.17  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.94/2.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------