%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : COL021-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n021.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 04:48:48 EDT 2024

% Result   : Unsatisfiable 2.50s 1.56s
% Output   : Refutation 2.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   14 (   9 unt;   5 typ;   0 def)
%            Number of atoms       :    9 (   8 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   54 (   2   ~;   0   |;   0   &;  52   @)
%                                         (   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     :    7 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

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

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

thf(b_type,type,
    b: $i ).

thf(m_type,type,
    m: $i ).

thf(v_type,type,
    v: $i ).

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

thf(5,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 @ b @ A ) @ B ) @ C )
      = ( apply @ A @ ( apply @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
      = ( apply @ A @ ( apply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( apply @ m @ A )
      = ( apply @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).

thf(10,plain,
    ! [A: $i] :
      ( ( apply @ m @ A )
      = ( apply @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ v @ A ) @ B ) @ C )
      = ( apply @ ( apply @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_definition) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ v @ A ) @ B ) @ C )
      = ( apply @ ( apply @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(18,plain,
    $false,
    inference(e,[status(thm)],[5,8,10,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : COL021-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Jun 18 15:47:10 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.98  % [INFO] 	 Parsing done (103ms). 
% 1.23/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.54/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.71/1.25  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.71/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.71/1.26  % [INFO] 	 Type checking passed. 
% 1.71/1.26  % [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 ... 
% 2.50/1.56  % External prover 'e' found a proof!
% 2.50/1.56  % [INFO] 	 Killing All external provers ... 
% 2.50/1.56  % Time passed: 1018ms (effective reasoning time: 567ms)
% 2.50/1.56  % Axioms used in derivation (3): b_definition, m_definition, v_definition
% 2.50/1.56  % No. of inferences in proof: 9
% 2.50/1.56  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1018 ms resp. 567 ms w/o parsing
% 2.50/1.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.50/1.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------