%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO368^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 09:00:01 EDT 2024

% Result   : Theorem 2.51s 1.89s
% Output   : Refutation 2.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   14 (   6 unt;   3 typ;   0 def)
%            Number of atoms       :   43 (   8 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   22 (   6   ~;   0   |;   3   &;  10   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $o ).

thf(cP_type,type,
    cP: $o > $o ).

thf(a_type,type,
    a: $o ).

thf(1,conjecture,
    ( ( ( a = b )
      & ( cP @ a ) )
   => ( cP @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTRIVEXT1) ).

thf(2,negated_conjecture,
    ~ ( ( ( a = b )
        & ( cP @ a ) )
     => ( cP @ b ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ( a = b )
        & ( cP @ a ) )
     => ( cP @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    cP @ a,
    inference(cnf,[status(esa)],[3]) ).

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

thf(8,plain,
    ( ( cP @ a )
   != ( cP @ b ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(9,plain,
    a != b,
    inference(simp,[status(thm)],[8]) ).

thf(6,plain,
    a = b,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    a = b,
    inference(lifteq,[status(thm)],[6]) ).

thf(13,plain,
    b != b,
    inference(rewrite,[status(thm)],[9,7]) ).

thf(14,plain,
    $false,
    inference(simp,[status(thm)],[13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SYO368^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.10/0.32  % Computer : n025.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon May 20 09:37:24 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.99/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.09  % [INFO] 	 Parsing done (152ms). 
% 1.25/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.46  % [INFO] 	 nitpick registered as external prover. 
% 1.84/1.46  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.53  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.99/1.56  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.99/1.56  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.99/1.57  % [INFO] 	 Type checking passed. 
% 1.99/1.57  % [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 ... 
% 2.51/1.88  % [INFO] 	 Killing All external provers ... 
% 2.51/1.89  % Time passed: 1415ms (effective reasoning time: 776ms)
% 2.51/1.89  % 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)>
% 2.51/1.89  % Axioms used in derivation (0): 
% 2.51/1.89  % No. of inferences in proof: 11
% 2.51/1.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1415 ms resp. 776 ms w/o parsing
% 2.51/1.91  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.51/1.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------