%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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  7 10:45:07 EDT 2024

% Result   : Theorem 2.34s 1.73s
% Output   : Refutation 2.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   12 (   8 unt;   4 typ;   0 def)
%            Number of atoms       :    8 (   7 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   40 (  12   ~;   0   |;   0   &;  28   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0   ^   6   !;   1   ?;   7   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(x_type,type,
    x: nat ).

thf(y_type,type,
    y: nat ).

thf(pl_type,type,
    pl: nat > nat > nat ).

thf(1,conjecture,
    ~ ! [A: nat] :
        ( ( pl @ x @ y )
       != ( pl @ x @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18) ).

thf(2,negated_conjecture,
    ~ ~ ! [A: nat] :
          ( ( pl @ x @ y )
         != ( pl @ x @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ~ ! [A: nat] :
          ( ( pl @ x @ y )
         != ( pl @ x @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [A: nat] :
      ( ( pl @ x @ y )
     != ( pl @ x @ A ) ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ~ ? [A: nat] :
        ( ( pl @ x @ y )
        = ( pl @ x @ A ) ),
    inference(miniscope,[status(thm)],[4]) ).

thf(6,plain,
    ! [A: nat] :
      ( ( pl @ x @ y )
     != ( pl @ x @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(7,plain,
    ! [A: nat] :
      ( ( pl @ x @ y )
     != ( pl @ x @ A ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(9,plain,
    $false,
    inference(pattern_uni,[status(thm)],[7:[bind(A,$thf( y ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.12/0.31  % Computer : n016.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Mon May  6 19:41:54 EDT 2024
% 0.12/0.31  % CPUTime  : 
% 0.92/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.08  % [INFO] 	 Parsing done (212ms). 
% 1.31/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.41  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.48  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.98/1.51  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.98/1.51  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.98/1.51  % [INFO] 	 Type checking passed. 
% 1.98/1.52  % [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 ... 
% 2.34/1.72  % [INFO] 	 Killing All external provers ... 
% 2.34/1.73  % Time passed: 1287ms (effective reasoning time: 610ms)
% 2.34/1.73  % 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)>
% 2.34/1.73  % Axioms used in derivation (0): 
% 2.34/1.73  % No. of inferences in proof: 8
% 2.34/1.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1287 ms resp. 610 ms w/o parsing
% 2.34/1.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.34/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------