%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO378^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 09:00:03 EDT 2024

% Result   : Theorem 2.92s 2.07s
% Output   : Refutation 3.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   14 (  12 unt;   2 typ;   1 def)
%            Number of atoms       :   24 (  19 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :   35 (  13   ~;   4   |;   6   &;  12   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (  10   ^  11   !;   9   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_type,type,
    c: $i ).

thf(cQDP2_type,type,
    cQDP2: ( ( $i > $o ) > $o ) > $o ).

thf(cQDP2_def,definition,
    ( cQDP2
    = ( ^ [A: ( $i > $o ) > $o] :
          ( ( A = cQDP1 )
          & ? [B: $i > $o] : ( A @ B ) ) ) ) ).

thf(1,conjecture,
    ? [A: ( $i > $o ) > $o] : ( cQDP2 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDTHM2) ).

thf(2,negated_conjecture,
    ~ ? [A: ( $i > $o ) > $o] : ( cQDP2 @ A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ! [B: $i > $o,A: ( $i > $o ) > $o] :
      ( ( A
       != ( ^ [C: $i > $o] :
              ( ( C
                = ( ^ [D: $i] : ( D = c ) ) )
              & ? [D: $i] : ( C @ D ) ) ) )
      | ~ ( A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [B: $i > $o,A: ( $i > $o ) > $o] :
      ( ( A
       != ( ^ [C: $i > $o] :
              ( ( C
                = ( ^ [D: $i] : ( D = c ) ) )
              & ? [D: $i] : ( C @ D ) ) ) )
      | ~ ( A @ B ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ! [A: $i > $o] :
      ~ ( ( A
          = ( ^ [B: $i] : ( B = c ) ) )
        & ? [B: $i] : ( A @ B ) ),
    inference(simp,[status(thm)],[5]) ).

thf(7,plain,
    ! [B: $i,A: $i > $o] :
      ( ( A
       != ( ^ [C: $i] : ( C = c ) ) )
      | ~ ( A @ B ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ! [B: $i,A: $i > $o] :
      ( ( A
       != ( ^ [C: $i] : ( C = c ) ) )
      | ~ ( A @ B ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(10,plain,
    ! [A: $i] : ( A != c ),
    inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( ^ [C: $i] : ( C = c ) )),bind(B,$thf( B ))]]) ).

thf(16,plain,
    ! [A: $i] : ( A != c ),
    inference(lifteq,[status(thm)],[10]) ).

thf(18,plain,
    $false,
    inference(simp,[status(thm)],[16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SYO378^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.02/0.13  % Command  : run_Leo-III %s %d
% 0.11/0.33  % Computer : n023.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon May 20 10:16:54 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.98/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.27/1.12  % [INFO] 	 Parsing done (165ms). 
% 1.27/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.84/1.50  % [INFO] 	 nitpick registered as external prover. 
% 1.84/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.00/1.63  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.63  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.63  % [INFO] 	 Type checking passed. 
% 2.16/1.64  % [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 ... 
% 2.92/2.06  % [INFO] 	 Killing All external provers ... 
% 2.92/2.07  % Time passed: 1586ms (effective reasoning time: 926ms)
% 2.92/2.07  % 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)>
% 2.92/2.07  % Axioms used in derivation (0): 
% 2.92/2.07  % No. of inferences in proof: 11
% 2.92/2.07  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1586 ms resp. 926 ms w/o parsing
% 3.18/2.16  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/2.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------