%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 03:39:00 EDT 2024

% Result   : Theorem 2.25s 1.37s
% Output   : Refutation 2.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   5 unt;   4 typ;   3 def)
%            Number of atoms       :   31 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :   66 (   2   ~;   0   |;   1   &;  54   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   8 con; 0-4 aty)
%            Number of variables   :   23 (  10   ^  13   !;   0   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(func_type,type,
    func: $i > $i > $i > $o ).

thf(func_def,definition,
    ( func
    = ( ^ [A: $i,B: $i,C: $i] :
          ( ( breln @ A @ B @ C )
          & ! [D: $i] :
              ( ( in @ D @ A )
             => ( ex1 @ B
                @ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).

thf(apProp_type,type,
    apProp: $o ).

thf(apProp_def,definition,
    ( apProp
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( func @ A @ B @ C )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ B
                    @ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) )
                @ B ) ) ) ) ) ).

thf(ap_type,type,
    ap: $i > $i > $i > $i > $i ).

thf(ap_def,definition,
    ( ap
    = ( ^ [A: $i,B: $i,C: $i,D: $i] :
          ( setunion
          @ ( dsetconstr @ B
            @ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ).

thf(1,conjecture,
    ( apProp
   => ! [A: $i,B: $i,C: $i] :
        ( ( func @ A @ B @ C )
       => ! [D: $i] :
            ( ( in @ D @ A )
           => ( in @ ( ap @ A @ B @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).

thf(2,negated_conjecture,
    ~ ( apProp
     => ! [A: $i,B: $i,C: $i] :
          ( ( func @ A @ B @ C )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( in @ ( ap @ A @ B @ C @ D ) @ B ) ) ) ),
    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
% 0.03/0.12  % Problem  : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n008.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
% 0.16/0.37  % DateTime : Sun May 19 16:15:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (101ms). 
% 1.32/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.97/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.97/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.97/1.28  % [INFO] 	 Type checking passed. 
% 1.97/1.28  % [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 ... 
% 2.25/1.37  % [INFO] 	 Killing All external provers ... 
% 2.25/1.37  % Time passed: 830ms (effective reasoning time: 384ms)
% 2.25/1.37  % 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)>
% 2.25/1.37  % Axioms used in derivation (0): 
% 2.25/1.37  % No. of inferences in proof: 4
% 2.25/1.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 830 ms resp. 384 ms w/o parsing
% 2.25/1.40  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.25/1.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------