%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n028.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 : Mon Jun 24 14:42:20 EDT 2024

% Result   : Theorem 3.09s 1.65s
% Output   : Refutation 3.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    7 (   4 unt;   0 typ;   3 def)
%            Number of atoms       :   23 (   7 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   48 (   2   ~;   0   |;   7   &;  37   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-3 aty)
%            Number of variables   :   23 (   8   ^  11   !;   4   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
thf(intersection_type,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(intersection_def,definition,
    ( intersection
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(subset_type,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

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

thf(fun_image_type,type,
    fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

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

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o,C: $i > $i] : ( subset @ ( fun_image @ C @ ( intersection @ A @ B ) ) @ ( intersection @ ( fun_image @ C @ A ) @ ( fun_image @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $o,B: $i > $o,C: $i > $i] : ( subset @ ( fun_image @ C @ ( intersection @ A @ B ) ) @ ( intersection @ ( fun_image @ C @ A ) @ ( fun_image @ C @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(23,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 16:58:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.92/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/0.98  % [INFO] 	 Parsing done (130ms). 
% 1.35/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.19  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.02/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.02/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.29  % [INFO] 	 Type checking passed. 
% 2.02/1.29  % [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 ... 
% 3.09/1.65  % External prover 'e' found a proof!
% 3.09/1.65  % [INFO] 	 Killing All external provers ... 
% 3.09/1.65  % Time passed: 1126ms (effective reasoning time: 652ms)
% 3.09/1.65  % 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)>
% 3.09/1.65  % Axioms used in derivation (0): 
% 3.09/1.65  % No. of inferences in proof: 4
% 3.09/1.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1126 ms resp. 652 ms w/o parsing
% 3.09/1.67  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.09/1.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------