%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : COL019-1 : TPTP v8.1.2. Released v1.0.0.
% 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  7 07:29:14 EDT 2024

% Result   : Unsatisfiable 3.05s 1.72s
% Output   : Refutation 3.05s
% 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 :   62 (   2   ~;   0   |;   0   &;  60   @)
%                                         (   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   :   18 (   0   ^  18   !;   0   ?;  18   :)

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

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

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

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

thf(t_type,type,
    t: $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 @ s @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).

thf(8,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,
    ! [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(10,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)],[3]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( apply @ ( apply @ t @ A ) @ B )
      = ( apply @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).

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

thf(22,plain,
    $false,
    inference(e,[status(thm)],[5,8,10,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COL019-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n025.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 14:04:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 1.03/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.04  % [INFO] 	 Parsing done (120ms). 
% 1.31/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.32  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.95/1.34  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.95/1.35  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.95/1.35  % [INFO] 	 Type checking passed. 
% 1.95/1.35  % [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 ... 
% 3.05/1.72  % External prover 'e' found a proof!
% 3.05/1.72  % [INFO] 	 Killing All external provers ... 
% 3.05/1.72  % Time passed: 1200ms (effective reasoning time: 670ms)
% 3.05/1.72  % 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)>
% 3.05/1.72  % Axioms used in derivation (3): s_definition, b_definition, t_definition
% 3.05/1.72  % No. of inferences in proof: 9
% 3.05/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1200 ms resp. 670 ms w/o parsing
% 3.05/1.77  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------