%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : COL001-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n007.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 04:48:39 EDT 2024

% Result   : Unsatisfiable 3.15s 2.15s
% Output   : Refutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   11 (   7 unt;   4 typ;   0 def)
%            Number of atoms       :    7 (   6 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   38 (   2   ~;   0   |;   0   &;  36   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(apply_type,type,
    apply: $i > $i > $i ).

thf(combinator_type,type,
    combinator: $i ).

thf(s_type,type,
    s: $i ).

thf(k_type,type,
    k: $i ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( A
     != ( apply @ combinator @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).

thf(4,plain,
    ! [A: $i] :
      ( A
     != ( apply @ combinator @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( apply @ ( apply @ k @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( apply @ ( apply @ k @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(19,plain,
    $false,
    inference(e,[status(thm)],[4,7,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : COL001-1 : TPTP v8.2.0. Released v1.0.0.
% 0.00/0.10  % Command  : run_Leo-III %s %d THM
% 0.10/0.31  % Computer : n007.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue Jun 18 16:30:10 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 1.04/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/1.12  % [INFO] 	 Parsing done (153ms). 
% 1.37/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.50  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.06/1.62  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.06/1.63  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.06/1.63  % [INFO] 	 Type checking passed. 
% 2.06/1.63  % [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 ... 
% 3.15/2.15  % External prover 'e' found a proof!
% 3.15/2.15  % [INFO] 	 Killing All external provers ... 
% 3.15/2.15  % Time passed: 1662ms (effective reasoning time: 1004ms)
% 3.15/2.15  % Axioms used in derivation (2): s_definition, k_definition
% 3.15/2.15  % No. of inferences in proof: 7
% 3.15/2.15  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1662 ms resp. 1004 ms w/o parsing
% 3.15/2.19  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/2.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------