%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET684^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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  7 10:50:21 EDT 2024

% Result   : Theorem 2.61s 1.61s
% Output   : Refutation 2.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    6 (   5 unt;   1 typ;   1 def)
%            Number of atoms       :    8 (   3 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   25 (   2   ~;   0   |;   3   &;  20   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1 usr;   2 con; 0-4 aty)
%            Number of variables   :   15 (   4   ^   8   !;   3   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(rel_composition_type,type,
    rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).

thf(rel_composition_def,definition,
    ( rel_composition
    = ( ^ [A: $i > $i > $o,B: $i > $i > $o,C: $i,D: $i] :
        ? [E: $i] :
          ( ( A @ C @ E )
          & ( B @ E @ D ) ) ) ) ).

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

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

thf(3,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    $false,
    inference(simp,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET684^3 : TPTP v8.1.2. Released v3.6.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n006.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May  6 20:46:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.98/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.43/1.09  % [INFO] 	 Parsing done (195ms). 
% 1.43/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.99/1.36  % [INFO] 	 nitpick registered as external prover. 
% 1.99/1.36  % [INFO] 	 Scanning for conjecture ... 
% 2.26/1.48  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.36/1.50  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.36/1.51  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.36/1.51  % [INFO] 	 Type checking passed. 
% 2.36/1.51  % [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 ... 
% 2.61/1.61  % [INFO] 	 Killing All external provers ... 
% 2.61/1.61  % Time passed: 1107ms (effective reasoning time: 507ms)
% 2.61/1.61  % 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)>
% 2.61/1.61  % Axioms used in derivation (0): 
% 2.61/1.61  % No. of inferences in proof: 4
% 2.61/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1107 ms resp. 507 ms w/o parsing
% 2.61/1.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.61/1.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------