TSTP Solution File: SEU550^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU550^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 03:42:38 EDT 2024

% Result   : Theorem 2.38s 1.48s
% Output   : Refutation 2.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (   6 unt;   3 typ;   1 def)
%            Number of atoms       :   51 (  27 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :   67 (   7   ~;   2   |;   9   &;  34   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   36 (   1   ^  26   !;   9   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(exu_type,type,
    exu: ( $i > $o ) > $o ).

thf(exu_def,definition,
    ( exu
    = ( ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ! [C: $i] :
              ( ( A @ C )
             => ( B = C ) ) ) ) ) ).

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

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

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o] :
      ( ! [C: $i,D: $i] :
          ( ( C = D )
         => ( ( A @ C )
            = ( B @ D ) ) )
     => ( ( exu @ A )
        = ( exu @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).

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

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

thf(4,plain,
    ( ( ? [A: $i] :
          ( ( sk1 @ A )
          & ! [B: $i] :
              ( ( sk1 @ B )
             => ( A = B ) ) ) )
   != ( ? [A: $i] :
          ( ( sk2 @ A )
          & ! [B: $i] :
              ( ( sk2 @ B )
             => ( A = B ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ( ? [A: $i] :
          ( ( sk2 @ A )
          & ! [B: $i] :
              ( ( sk2 @ B )
             => ( A = B ) ) ) )
   != ( ? [A: $i] :
          ( ( sk1 @ A )
          & ! [B: $i] :
              ( ( sk1 @ B )
             => ( A = B ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( ( sk1 @ A )
        = ( sk2 @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( ( sk1 @ A )
        = ( sk2 @ B ) ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( sk2 @ A )
      = ( sk1 @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ? [A: $i] :
          ( ( sk1 @ A )
          & ! [B: $i] :
              ( ( sk1 @ B )
             => ( A = B ) ) ) )
   != ( ? [A: $i] :
          ( ( sk1 @ A )
          & ! [B: $i] :
              ( ( sk1 @ B )
             => ( A = B ) ) ) ) ),
    inference(rewrite,[status(thm)],[6,8]) ).

thf(12,plain,
    $false,
    inference(simp,[status(thm)],[11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU550^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 15:37:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.84/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/0.95  % [INFO] 	 Parsing done (97ms). 
% 1.17/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.44/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.44/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.82/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.82/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.24  % [INFO] 	 Type checking passed. 
% 1.82/1.24  % [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 ... 
% 2.38/1.47  % [INFO] 	 Killing All external provers ... 
% 2.38/1.48  % Time passed: 950ms (effective reasoning time: 510ms)
% 2.38/1.48  % 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)>
% 2.38/1.48  % Axioms used in derivation (0): 
% 2.38/1.48  % No. of inferences in proof: 10
% 2.38/1.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 950 ms resp. 510 ms w/o parsing
% 2.64/1.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.64/1.54  % [INFO] 	 Killing All external provers ... 
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