%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET630^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 03:03:19 EDT 2024

% Result   : Theorem 3.31s 2.11s
% Output   : Refutation 3.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   10 (   4 unt;   3 typ;   3 def)
%            Number of atoms       :   13 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   44 (   8   ~;   2   |;   8   &;  26   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-3 aty)
%            Number of variables   :   16 (   8   ^   6   !;   2   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(excl_union_type,type,
    excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(excl_union_def,definition,
    ( excl_union
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( ( A @ C )
            & ~ ( B @ C ) )
          | ( ~ ( A @ C )
            & ( B @ C ) ) ) ) ) ).

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(misses_type,type,
    misses: ( $i > $o ) > ( $i > $o ) > $o ).

thf(misses_def,definition,
    ( misses
    = ( ^ [A: $i > $o,B: $i > $o] :
          ~ ? [C: $i] :
              ( ( A @ C )
              & ( B @ C ) ) ) ) ).

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o] : ( misses @ ( intersection @ A @ B ) @ ( excl_union @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

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

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

thf(11,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET630^3 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n022.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon May 20 11:06:54 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.99/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/1.17  % [INFO] 	 Parsing done (195ms). 
% 1.51/1.19  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.56  % [INFO] 	 eprover registered as external prover. 
% 2.04/1.56  % [INFO] 	 cvc4 registered as external prover. 
% 2.04/1.57  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.69  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.40/1.71  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.40/1.72  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.40/1.72  % [INFO] 	 Type checking passed. 
% 2.40/1.72  % [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 ... 
% 3.20/2.11  % External prover 'cvc4' found a proof!
% 3.20/2.11  % [INFO] 	 Killing All external provers ... 
% 3.20/2.11  % Time passed: 1629ms (effective reasoning time: 907ms)
% 3.20/2.11  % 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)>
% 3.31/2.11  % Axioms used in derivation (0): 
% 3.31/2.11  % No. of inferences in proof: 4
% 3.31/2.11  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1629 ms resp. 907 ms w/o parsing
% 3.32/2.14  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.32/2.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------