%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 03:38:44 EDT 2024

% Result   : Theorem 3.06s 1.70s
% Output   : Refutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   4 unt;   8 typ;   3 def)
%            Number of atoms       :   32 (   5 equ;   0 cnn)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives :   70 (   2   ~;   0   |;   2   &;  49   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^  17   !;   2   ?;  19   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(setunion_type,type,
    setunion: $i > $i ).

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

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

thf(subsetI2_type,type,
    subsetI2: $o ).

thf(subsetI2_def,definition,
    ( subsetI2
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf(setunionE2_type,type,
    setunionE2: $o ).

thf(setunionE2_def,definition,
    ( setunionE2
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ? [C: $i] :
              ( ( in @ C @ A )
              & ( in @ B @ C ) ) ) ) ) ).

thf(1,conjecture,
    ( uniqinunit
   => ( subsetI2
     => ( setunionE2
       => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).

thf(2,negated_conjecture,
    ~ ( uniqinunit
     => ( subsetI2
       => ( setunionE2
         => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(52,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n024.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 15:27:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.92/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.96  % [INFO] 	 Parsing done (106ms). 
% 1.22/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.28  % [INFO] 	 Type checking passed. 
% 1.88/1.28  % [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 ... 
% 3.06/1.69  % External prover 'e' found a proof!
% 3.06/1.70  % [INFO] 	 Killing All external provers ... 
% 3.06/1.70  % Time passed: 1177ms (effective reasoning time: 725ms)
% 3.06/1.70  % 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)>
% 3.06/1.70  % Axioms used in derivation (0): 
% 3.06/1.70  % No. of inferences in proof: 4
% 3.06/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1177 ms resp. 725 ms w/o parsing
% 3.06/1.71  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------