%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET086^1 : TPTP v8.1.2. Released v3.6.0.
% 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 : Tue May  7 10:49:07 EDT 2024

% Result   : Theorem 2.24s 1.40s
% Output   : Refutation 2.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    9 (   7 unt;   2 typ;   1 def)
%            Number of atoms       :    9 (   5 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    8 (   4   ~;   0   |;   0   &;   4   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   2   ^   5   !;   3   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(singleton_type,type,
    singleton: $i > $i > $o ).

thf(singleton_def,definition,
    ( singleton
    = ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).

thf(sk1_type,type,
    sk1: $i ).

thf(1,conjecture,
    ! [A: $i] :
    ? [B: $i] : ( singleton @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
      ? [B: $i] : ( singleton @ A @ B ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i] :
      ? [B: $i] : ( B = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [A: $i] : ( A != sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [A: $i] : ( A != sk1 ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    $false,
    inference(simp,[status(thm)],[5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET086^1 : TPTP v8.1.2. Released v3.6.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n007.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 20:30:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/0.99  % [INFO] 	 Parsing done (123ms). 
% 1.16/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.28  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.88/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.30  % [INFO] 	 Type checking passed. 
% 1.88/1.30  % [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 ... 
% 2.24/1.40  % [INFO] 	 Killing All external provers ... 
% 2.24/1.40  % Time passed: 858ms (effective reasoning time: 394ms)
% 2.24/1.40  % 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)>
% 2.24/1.40  % Axioms used in derivation (0): 
% 2.24/1.40  % No. of inferences in proof: 6
% 2.24/1.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 858 ms resp. 394 ms w/o parsing
% 2.24/1.42  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.24/1.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------