%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO218^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 08:56:09 EDT 2024

% Result   : Theorem 2.70s 1.53s
% Output   : Refutation 2.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   4 unt;   2 typ;   0 def)
%            Number of atoms       :   27 (  26 equ;  10 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   44 (   6   ~;   2   |;   0   &;  30   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   4 con; 0-2 aty)
%            Number of variables   :   11 (   0   ^  11   !;   0   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk1_type,type,
    sk1: $i ).

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ! [C: ( $i > $o ) > $i] :
          ( ( A
            = ( C @ ( (=) @ $i @ A ) ) )
         => ( B
            = ( C @ ( (=) @ $i @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM7B_pme) ).

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

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

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

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

thf(8,plain,
    sk2 = sk1,
    inference(pre_uni,[status(thm)],[7:[bind(A,$thf( ^ [B: $i > $o] : sk1 ))]]) ).

thf(4,plain,
    sk1 != sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    sk2 != sk1,
    inference(lifteq,[status(thm)],[4]) ).

thf(27,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[8,6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SYO218^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.08  % Command  : run_Leo-III %s %d
% 0.07/0.27  % Computer : n011.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Mon May 20 10:47:54 EDT 2024
% 0.07/0.27  % CPUTime  : 
% 0.72/0.74  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.08/0.85  % [INFO] 	 Parsing done (110ms). 
% 1.08/0.86  % [INFO] 	 Running in sequential loop mode. 
% 1.44/1.09  % [INFO] 	 eprover registered as external prover. 
% 1.44/1.09  % [INFO] 	 cvc4 registered as external prover. 
% 1.53/1.09  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.14  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.71/1.16  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.71/1.16  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.71/1.16  % [INFO] 	 Type checking passed. 
% 1.71/1.16  % [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 ... 
% 2.70/1.53  % [INFO] 	 Killing All external provers ... 
% 2.70/1.53  % Time passed: 1173ms (effective reasoning time: 668ms)
% 2.70/1.53  % 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)>
% 2.70/1.53  % Axioms used in derivation (0): 
% 2.70/1.53  % No. of inferences in proof: 9
% 2.70/1.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1173 ms resp. 668 ms w/o parsing
% 2.70/1.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.70/1.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------