%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO237^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 08:59:41 EDT 2024

% Result   : Theorem 3.03s 2.12s
% Output   : Refutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   18 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   23 (   9 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   43 (   7   ~;   0   |;   0   &;  27   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    5 (   0   ^   5   !;   0   ?;   5   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_type,type,
    g: $i > $i ).

thf(p_type,type,
    p: ( $i > $i ) > $o ).

thf(x_type,type,
    x: $i ).

thf(q_type,type,
    q: $i > $o ).

thf(f_type,type,
    f: $i > $i ).

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

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( f @ A )
        = ( g @ A ) )
   => ( ( p @ f )
     => ( ( q @ x )
       => ( p @ g ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM508) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( f @ A )
          = ( g @ A ) )
     => ( ( p @ f )
       => ( ( q @ x )
         => ( p @ g ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i] :
          ( ( f @ A )
          = ( g @ A ) )
     => ( ( p @ f )
       => ( ( q @ x )
         => ( p @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    p @ f,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( p @ g ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( p @ f )
   != ( p @ g ) ),
    inference(paramod_ordered,[status(thm)],[6,4]) ).

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

thf(11,plain,
    ( ( f @ sk1 )
   != ( g @ sk1 ) ),
    inference(func_ext,[status(esa)],[10]) ).

thf(7,plain,
    ! [A: $i] :
      ( ( f @ A )
      = ( g @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( f @ A )
      = ( g @ A ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(15,plain,
    ( ( g @ sk1 )
   != ( g @ sk1 ) ),
    inference(rewrite,[status(thm)],[11,8]) ).

thf(16,plain,
    $false,
    inference(simp,[status(thm)],[15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYO237^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May 20 09:03:39 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.06/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/1.15  % [INFO] 	 Parsing done (159ms). 
% 1.36/1.16  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.52  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.53  % [INFO] 	 Scanning for conjecture ... 
% 2.04/1.62  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.16/1.65  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.16/1.65  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.66  % [INFO] 	 Type checking passed. 
% 2.16/1.66  % [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 ... 
% 2.90/2.08  % [INFO] 	 Killing All external provers ... 
% 2.90/2.08  % Time passed: 1582ms (effective reasoning time: 916ms)
% 2.90/2.08  % 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)>
% 3.03/2.12  % Axioms used in derivation (0): 
% 3.03/2.12  % No. of inferences in proof: 12
% 3.03/2.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1582 ms resp. 916 ms w/o parsing
% 3.03/2.16  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/2.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------