%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO359^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 08:56:30 EDT 2024

% Result   : Theorem 2.85s 1.75s
% Output   : Refutation 2.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   16 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   55 (  16 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :   52 (   6   ~;   0   |;   0   &;  34   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $tType ).

thf(gtype_type,type,
    gtype: $tType ).

thf(g_type,type,
    g: b > $o ).

thf(h_type,type,
    h: ( b > $o ) > gtype ).

thf(f_type,type,
    f: b > $o ).

thf(1,conjecture,
    ( ( ! [A: b] :
          ( ( f @ A )
          = ( g @ A ) )
     => ! [A: ( b > $o ) > $o] :
          ( ( A @ f )
         => ( A @ g ) ) )
   => ( ! [A: b] :
          ( ( f @ A )
          = ( g @ A ) )
     => ( ( h @ f )
        = ( h @ g ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT1) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: b] :
            ( ( f @ A )
            = ( g @ A ) )
       => ! [A: ( b > $o ) > $o] :
            ( ( A @ f )
           => ( A @ g ) ) )
     => ( ! [A: b] :
            ( ( f @ A )
            = ( g @ A ) )
       => ( ( h @ f )
          = ( h @ g ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: b] :
            ( ( f @ A )
            = ( g @ A ) )
       => ! [A: ( b > $o ) > $o] :
            ( ( A @ f )
           => ( A @ g ) ) )
     => ( ! [A: b] :
            ( ( f @ A )
            = ( g @ A ) )
       => ( ( h @ f )
          = ( h @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( h @ f )
   != ( h @ g ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ( ( h @ f )
   != ( h @ g ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(14,plain,
    f != g,
    inference(simp,[status(thm)],[8]) ).

thf(5,plain,
    ! [A: b] :
      ( ( f @ A )
      = ( g @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: b] :
      ( ( f @ A )
      = ( g @ A ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(10,plain,
    ! [A: b] :
      ( ( f @ A )
      = ( g @ A ) ),
    inference(simp,[status(thm)],[9]) ).

thf(20,plain,
    g != g,
    inference(rewrite,[status(thm)],[14,10]) ).

thf(21,plain,
    $false,
    inference(simp,[status(thm)],[20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYO359^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 09:43:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.97/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.07/1.01  % [INFO] 	 Parsing done (114ms). 
% 1.07/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.71/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.71/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.71/1.33  % [INFO] 	 Type checking passed. 
% 1.96/1.33  % [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 ... 
% 2.85/1.74  % [INFO] 	 Killing All external provers ... 
% 2.85/1.74  % Time passed: 1239ms (effective reasoning time: 722ms)
% 2.85/1.74  % 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)>
% 2.85/1.74  % Axioms used in derivation (0): 
% 2.85/1.74  % No. of inferences in proof: 11
% 2.85/1.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1239 ms resp. 722 ms w/o parsing
% 2.85/1.77  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.85/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------