%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : ALG282^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n020.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 04:01:42 EDT 2024

% Result   : Theorem 3.46s 2.32s
% Output   : Refutation 3.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :   13 (  12 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   56 (   2   ~;   0   |;   6   &;  45   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  21   !;   3   ?;  24   :)

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

thf(cP_type,type,
    cP: a > a > a ).

thf(cE_type,type,
    cE: a ).

thf(cJ_type,type,
    cJ: a > a ).

thf(1,conjecture,
    ( ( ! [A: a,B: a,C: a] :
          ( ( cP @ ( cP @ A @ B ) @ C )
          = ( cP @ A @ ( cP @ B @ C ) ) )
      & ! [A: a] :
          ( ( cP @ cE @ A )
          = A )
      & ! [A: a] :
          ( ( cP @ ( cJ @ A ) @ A )
          = cE ) )
   => ! [A: a,B: a] :
      ? [C: a] :
        ( ( cP @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM21_pme) ).

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

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

thf(17,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ALG282^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d THM
% 0.10/0.32  % Computer : n020.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 : Wed Jun 19 15:53:40 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 1.10/1.03  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.20  % [INFO] 	 Parsing done (167ms). 
% 1.43/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.62  % [INFO] 	 eprover registered as external prover. 
% 2.04/1.63  % [INFO] 	 Scanning for conjecture ... 
% 2.22/1.72  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.22/1.76  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.22/1.76  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.22/1.77  % [INFO] 	 Type checking passed. 
% 2.22/1.77  % [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 ... 
% 3.46/2.31  % External prover 'e' found a proof!
% 3.46/2.31  % [INFO] 	 Killing All external provers ... 
% 3.46/2.31  % Time passed: 1807ms (effective reasoning time: 1093ms)
% 3.46/2.31  % 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)>
% 3.46/2.32  % Axioms used in derivation (0): 
% 3.46/2.32  % No. of inferences in proof: 4
% 3.46/2.32  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1807 ms resp. 1093 ms w/o parsing
% 3.46/2.35  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/2.35  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------