%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV228^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n019.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 15:58:33 EDT 2024

% Result   : Theorem 3.36s 1.84s
% Output   : Refutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   12 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :   25 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   54 (  12   ~;   3   |;   3   &;  30   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   13 (   2   ^   8   !;   3   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cS_type,type,
    cS: a > $o ).

thf(sk1_type,type,
    sk1: a ).

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

thf(1,conjecture,
    ! [A: a] :
      ( ( cS @ A )
     => ? [B: a > $o] :
          ( ! [C: a] :
              ( ( B @ C )
             => ( cS @ C ) )
          & ( B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM91A_pme) ).

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

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

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

thf(6,plain,
    cS @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: a > $o] :
      ( ~ ( cS @ ( sk2 @ A ) )
      | ( ( cS @ sk1 )
       != ( A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,5]) ).

thf(19,plain,
    ~ ( cS @ ( sk2 @ cS ) ),
    inference(pre_uni,[status(thm)],[8:[bind(A,$thf( cS ))]]) ).

thf(28,plain,
    ( ( cS @ ( sk2 @ cS ) )
   != ( cS @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[6,19]) ).

thf(29,plain,
    ( ( sk2 @ cS )
   != sk1 ),
    inference(simp,[status(thm)],[28]) ).

thf(13,plain,
    ( ~ ( cS
        @ ( sk2
          @ ^ [A: a] : $true ) )
    | ~ $true ),
    inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [B: a] : $true ))]]) ).

thf(27,plain,
    ~ ( cS
      @ ( sk2
        @ ^ [A: a] : $true ) ),
    inference(simp,[status(thm)],[13]) ).

thf(65,plain,
    $false,
    inference(e,[status(thm)],[5,29,6,27,3,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV228^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n019.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 : Fri Jun 21 19:39:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/0.98  % [INFO] 	 Parsing done (111ms). 
% 1.09/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.61/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.79/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.79/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.79/1.27  % [INFO] 	 Type checking passed. 
% 1.79/1.27  % [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 ... 
% 3.36/1.83  % External prover 'e' found a proof!
% 3.36/1.84  % [INFO] 	 Killing All external provers ... 
% 3.36/1.84  % Time passed: 1322ms (effective reasoning time: 841ms)
% 3.36/1.84  % 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)>
% 3.36/1.84  % Axioms used in derivation (0): 
% 3.36/1.84  % No. of inferences in proof: 12
% 3.36/1.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1322 ms resp. 841 ms w/o parsing
% 3.39/1.86  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------