%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET764^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 10:50:28 EDT 2024

% Result   : Theorem 2.53s 1.73s
% Output   : Refutation 2.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   6 unt;   2 typ;   2 def)
%            Number of atoms       :   16 (   5 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :    9 (   2   ~;   0   |;   1   &;   6   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-3 aty)
%            Number of variables   :    7 (   4   ^   2   !;   1   ?;   7   :)

% Comments : 
%------------------------------------------------------------------------------
thf(emptyset_type,type,
    emptyset: $i > $o ).

thf(emptyset_def,definition,
    ( emptyset
    = ( ^ [A: $i] : $false ) ) ).

thf(fun_inv_image_type,type,
    fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

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

thf(1,conjecture,
    ! [A: $i > $i] :
      ( ( fun_inv_image @ A @ emptyset )
      = emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i] :
        ( ( fun_inv_image @ A @ emptyset )
        = emptyset ),
    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
% 0.00/0.11  % Problem  : SET764^4 : TPTP v8.1.2. Released v3.6.0.
% 0.11/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon May  6 20:44:23 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.95/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.13  % [INFO] 	 Parsing done (215ms). 
% 1.32/1.14  % [INFO] 	 Running in sequential loop mode. 
% 2.01/1.47  % [INFO] 	 nitpick registered as external prover. 
% 2.04/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.15/1.58  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.15/1.60  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.15/1.60  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.15/1.60  % [INFO] 	 Type checking passed. 
% 2.15/1.60  % [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 ... 
% 2.53/1.73  % [INFO] 	 Killing All external provers ... 
% 2.53/1.73  % Time passed: 1243ms (effective reasoning time: 580ms)
% 2.53/1.73  % 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)>
% 2.53/1.73  % Axioms used in derivation (0): 
% 2.53/1.73  % No. of inferences in proof: 4
% 2.53/1.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1243 ms resp. 580 ms w/o parsing
% 2.53/1.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.53/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------