%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 03:38:04 EDT 2024

% Result   : Theorem 3.15s 1.72s
% Output   : Refutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   3 unt;   5 typ;   2 def)
%            Number of atoms       :   23 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   56 (   3   ~;   0   |;   3   &;  33   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^  16   !;   3   ?;  19   :)

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

thf(emptyset_type,type,
    emptyset: $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

thf(dsetconstrI_def,definition,
    ( dsetconstrI
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(emptysetE_def,definition,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ) ).

thf(1,conjecture,
    ( dsetconstrI
   => ( emptysetE
     => ! [A: $i,B: $i > $o] :
          ( ? [C: $i] :
              ( ( in @ C @ A )
              & ( B @ C ) )
         => ( ( ( dsetconstr @ A @ B )
              = emptyset )
           => $false ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrI
     => ( emptysetE
       => ! [A: $i,B: $i > $o] :
            ( ? [C: $i] :
                ( ( in @ C @ A )
                & ( B @ C ) )
           => ( ( ( dsetconstr @ A @ B )
                = emptyset )
             => $false ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(34,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 15:46:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.02/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.33/1.02  % [INFO] 	 Parsing done (115ms). 
% 1.33/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.74/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.74/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.33  % [INFO] 	 Type checking passed. 
% 2.02/1.33  % [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 ... 
% 3.15/1.72  % External prover 'e' found a proof!
% 3.15/1.72  % [INFO] 	 Killing All external provers ... 
% 3.15/1.72  % Time passed: 1201ms (effective reasoning time: 689ms)
% 3.15/1.72  % 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)>
% 3.15/1.72  % Axioms used in derivation (0): 
% 3.15/1.72  % No. of inferences in proof: 4
% 3.15/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1201 ms resp. 689 ms w/o parsing
% 3.15/1.74  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------