%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 : Fri May 19 11:53:37 EDT 2023

% Result   : Theorem 2.65s 1.62s
% Output   : Refutation 2.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   12 (   3 unt;   2 typ;   0 def)
%            Number of atoms       :   30 (   6 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   68 (   2   ~;   0   |;   8   &;  46   @)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^;  19   !;   0   ?;  19   :)

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

thf(member_type,type,
    member: $i > $i > $o ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_extensionality) ).

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

thf(6,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( subset @ A @ B )
          & ( subset @ B @ A ) )
       => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( subset @ A @ B )
        & ( subset @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

thf(11,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( subset @ A @ B )
          & ( subset @ B @ A ) ) )
      & ( ( ( subset @ A @ B )
          & ( subset @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( member @ C @ A )
         => ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

thf(29,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(31,plain,
    $false,
    inference(cvc4,[status(thm)],[6,11,22,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n023.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 19:06:00 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 1.01/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/0.98  % [INFO] 	 Parsing done (109ms). 
% 1.32/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.26  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.86/1.28  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.86/1.29  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.86/1.29  % [INFO] 	 Type checking passed. 
% 1.86/1.30  % [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 ... 
% 2.65/1.62  % External prover 'cvc4' found a proof!
% 2.65/1.62  % [INFO] 	 Killing All external provers ... 
% 2.65/1.62  % Time passed: 1080ms (effective reasoning time: 627ms)
% 2.65/1.62  % 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)>
% 2.65/1.62  % Axioms used in derivation (3): equal_defn, subset_defn, reflexivity_of_subset
% 2.65/1.62  % No. of inferences in proof: 10
% 2.65/1.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1080 ms resp. 627 ms w/o parsing
% 2.99/1.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.99/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------