%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU528^2 : TPTP v8.2.0. Released v3.7.0.
% 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 : Tue May 21 03:42:30 EDT 2024

% Result   : Theorem 3.07s 1.79s
% Output   : Refutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (   6 unt;   6 typ;   1 def)
%            Number of atoms       :   27 (  13 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   64 (  13   ~;   3   |;   0   &;  40   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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   :   16 (   0   ^  16   !;   0   ?;  16   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $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(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(1,conjecture,
    ( uniqinunit
   => ! [A: $i,B: $i] :
        ( ( A != B )
       => ~ ( in @ B @ ( setadjoin @ A @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).

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

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

thf(4,plain,
    in @ sk2 @ ( setadjoin @ sk1 @ emptyset ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( in @ sk2 @ ( setadjoin @ sk1 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4,8]) ).

thf(26,plain,
    sk2 = sk1,
    inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(5,plain,
    sk1 != sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    sk2 != sk1,
    inference(lifteq,[status(thm)],[5]) ).

thf(49,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[26,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU528^2 : TPTP v8.2.0. Released v3.7.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n023.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sun May 19 16:23:09 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.94/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/1.01  % [INFO] 	 Parsing done (105ms). 
% 1.16/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.90/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.90/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.90/1.37  % [INFO] 	 Type checking passed. 
% 1.90/1.38  % [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 ... 
% 3.07/1.79  % [INFO] 	 Killing All external provers ... 
% 3.07/1.79  % Time passed: 1221ms (effective reasoning time: 763ms)
% 3.07/1.79  % 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)>
% 3.07/1.79  % Axioms used in derivation (0): 
% 3.07/1.79  % No. of inferences in proof: 11
% 3.07/1.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1221 ms resp. 763 ms w/o parsing
% 3.07/1.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.07/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------