%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SYO233^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n017.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 : Mon Jun 24 20:50:43 EDT 2024

% Result   : Theorem 2.81s 1.67s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   11 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   12 (  11 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   43 (   8   ~;   3   |;   0   &;  26   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   11 (   0   ^  11   !;   0   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cN_type,type,
    cN: $i > $i ).

thf(cM_type,type,
    cM: $i > $i ).

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

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

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

thf(4,plain,
    cM != cN,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    cM != cN,
    inference(lifteq,[status(thm)],[4]) ).

thf(5,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ ( cM @ A ) )
      | ( B @ ( cN @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [A: $i] :
      ( ( ( cM @ A )
       != ( cM @ A ) )
      | ( ( cM @ A )
        = ( cN @ A ) ) ),
    inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ ( cM @ A ) ))]]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( ( cM @ A )
       != ( cM @ A ) )
      | ( ( cM @ A )
        = ( cN @ A ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(9,plain,
    ! [A: $i] :
      ( ( cM @ A )
      = ( cN @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(11,plain,
    cN != cN,
    inference(rewrite,[status(thm)],[7,9]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO233^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 06:32:55 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/0.99  % [INFO] 	 Parsing done (125ms). 
% 1.33/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.85/1.31  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.85/1.31  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.31  % [INFO] 	 Type checking passed. 
% 1.85/1.32  % [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 ... 
% 2.58/1.66  % [INFO] 	 Killing All external provers ... 
% 2.81/1.66  % Time passed: 1137ms (effective reasoning time: 655ms)
% 2.81/1.66  % 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)>
% 2.81/1.66  % Axioms used in derivation (0): 
% 2.81/1.66  % No. of inferences in proof: 11
% 2.81/1.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1137 ms resp. 655 ms w/o parsing
% 2.84/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.84/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------