%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 03:38:51 EDT 2024

% Result   : Theorem 3.13s 1.72s
% Output   : Refutation 3.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   13 (   4 unt;   6 typ;   3 def)
%            Number of atoms       :   27 (  11 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   62 (   2   ~;   0   |;   0   &;  46   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  21   !;   0   ?;  21   :)

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

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

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

thf(setadjoinIL_type,type,
    setadjoinIL: $o ).

thf(setadjoinIL_def,definition,
    ( setadjoinIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).

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

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

thf(secondinupair_type,type,
    secondinupair: $o ).

thf(secondinupair_def,definition,
    ( secondinupair
    = ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).

thf(1,conjecture,
    ( setadjoinIL
   => ( uniqinunit
     => ( secondinupair
       => ! [A: $i,B: $i,C: $i] :
            ( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
              = ( setadjoin @ C @ emptyset ) )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).

thf(2,negated_conjecture,
    ~ ( setadjoinIL
     => ( uniqinunit
       => ( secondinupair
         => ! [A: $i,B: $i,C: $i] :
              ( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
                = ( setadjoin @ C @ emptyset ) )
             => ( A = B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(17,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n021.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 : Sun May 19 16:41:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.01/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.99  % [INFO] 	 Parsing done (108ms). 
% 1.18/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.98/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.98/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.98/1.32  % [INFO] 	 Type checking passed. 
% 1.98/1.32  % [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 ... 
% 3.13/1.72  % External prover 'e' found a proof!
% 3.13/1.72  % [INFO] 	 Killing All external provers ... 
% 3.13/1.72  % Time passed: 1175ms (effective reasoning time: 712ms)
% 3.13/1.72  % 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)>
% 3.13/1.72  % Axioms used in derivation (0): 
% 3.13/1.72  % No. of inferences in proof: 4
% 3.13/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1175 ms resp. 712 ms w/o parsing
% 3.13/1.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.13/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------