TSTP Solution File: SEU463^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU463^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 03:37:43 EDT 2024

% Result   : Theorem 3.57s 1.94s
% Output   : Refutation 3.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   10 (   4 unt;   3 typ;   3 def)
%            Number of atoms       :   17 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  105 (   2   ~;   0   |;  16   &;  73   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-3 aty)
%            Number of variables   :   44 (   6   ^  38   !;   0   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(subrel_type,type,
    subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(subrel_def,definition,
    ( subrel
    = ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
        ! [C: $i,D: $i] :
          ( ( A @ C @ D )
         => ( B @ C @ D ) ) ) ) ).

thf(trans_type,type,
    trans: ( $i > $i > $o ) > $o ).

thf(trans_def,definition,
    ( trans
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

thf(tc_type,type,
    tc: ( $i > $i > $o ) > $i > $i > $o ).

thf(tc_def,definition,
    ( tc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
        ! [D: $i > $i > $o] :
          ( ( ( trans @ D )
            & ( subrel @ A @ D ) )
         => ( D @ B @ C ) ) ) ) ).

thf(1,conjecture,
    ! [A: $i > $i > $o,B: $i,C: $i,D: $i,E: $i > $i > $o] :
      ( ( ( trans @ E )
        & ( subrel @ A @ E )
        & ( tc @ A @ B @ C )
        & ( tc @ A @ C @ D ) )
     => ( E @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive3) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i,E: $i > $i > $o] :
        ( ( ( trans @ E )
          & ( subrel @ A @ E )
          & ( tc @ A @ B @ C )
          & ( tc @ A @ C @ D ) )
       => ( E @ B @ D ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(32,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU463^1 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun May 19 18:11:24 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.91/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.44/1.08  % [INFO] 	 Parsing done (171ms). 
% 1.44/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.34  % [INFO] 	 eprover registered as external prover. 
% 1.94/1.34  % [INFO] 	 cvc4 registered as external prover. 
% 1.94/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.21/1.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.31/1.49  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.31/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.31/1.49  % [INFO] 	 Type checking passed. 
% 2.31/1.50  % [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 ... 
% 3.57/1.94  % External prover 'e' found a proof!
% 3.57/1.94  % [INFO] 	 Killing All external provers ... 
% 3.57/1.94  % Time passed: 1390ms (effective reasoning time: 840ms)
% 3.57/1.94  % 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)>
% 3.57/1.94  % Axioms used in derivation (0): 
% 3.57/1.94  % No. of inferences in proof: 4
% 3.57/1.94  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1390 ms resp. 840 ms w/o parsing
% 3.65/1.97  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.65/1.97  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------