%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO226^5 : 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 08:59:38 EDT 2024

% Result   : Theorem 2.37s 1.48s
% Output   : Refutation 2.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   13 (   7 unt;   3 typ;   0 def)
%            Number of atoms       :   15 (  14 equ;   4 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   42 (   7   ~;   3   |;   0   &;  26   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   4 con; 0-2 aty)
%            Number of variables   :   13 (   0   ^  13   !;   0   ?;  13   :)

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

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

thf(sk3_type,type,
    sk3: ( $i > $i > $o ) > $i ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ! [C: $i > $i > $o] :
          ( ! [D: $i] : ( C @ D @ D )
         => ( C @ A @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47B) ).

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

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

thf(5,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( A @ ( sk3 @ A ) @ ( sk3 @ A ) )
      | ( A @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ( ( sk3 @ ( (=) @ $i ) )
     != ( sk3 @ ( (=) @ $i ) ) )
    | ( sk1 = sk2 ) ),
    inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ $i ))]]) ).

thf(8,plain,
    ( ( ( sk3 @ ( (=) @ $i ) )
     != ( sk3 @ ( (=) @ $i ) ) )
    | ( sk2 = sk1 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(9,plain,
    sk2 = sk1,
    inference(simp,[status(thm)],[8]) ).

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

thf(7,plain,
    sk2 != sk1,
    inference(lifteq,[status(thm)],[4]) ).

thf(10,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[9,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO226^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n005.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May 20 08:48:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.96/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.13/1.03  % [INFO] 	 Parsing done (103ms). 
% 1.35/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.78/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.78/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.78/1.30  % [INFO] 	 Type checking passed. 
% 1.78/1.30  % [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 ... 
% 2.30/1.47  % [INFO] 	 Killing All external provers ... 
% 2.30/1.48  % Time passed: 926ms (effective reasoning time: 436ms)
% 2.30/1.48  % 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)>
% 2.30/1.48  % Axioms used in derivation (0): 
% 2.30/1.48  % No. of inferences in proof: 10
% 2.37/1.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 926 ms resp. 436 ms w/o parsing
% 2.37/1.51  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.37/1.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------