%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : BOO011-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 May 20 18:57:22 EDT 2024

% Result   : Unsatisfiable 3.01s 1.83s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   17 (  12 unt;   4 typ;   0 def)
%            Number of atoms       :   14 (  13 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   31 (   5   ~;   1   |;   0   &;  25   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^   8   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(inverse_type,type,
    inverse: $i > $i ).

thf(additive_identity_type,type,
    additive_identity: $i ).

thf(multiplicative_identity_type,type,
    multiplicative_identity: $i ).

thf(add_type,type,
    add: $i > $i > $i ).

thf(8,axiom,
    ! [A: $i] :
      ( ( add @ A @ ( inverse @ A ) )
      = multiplicative_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).

thf(31,plain,
    ! [A: $i] :
      ( ( add @ A @ ( inverse @ A ) )
      = multiplicative_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(32,plain,
    ! [A: $i] :
      ( ( add @ A @ ( inverse @ A ) )
      = multiplicative_identity ),
    inference(lifteq,[status(thm)],[31]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( add @ additive_identity @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).

thf(45,plain,
    ! [A: $i] :
      ( ( add @ additive_identity @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(46,plain,
    ! [A: $i] :
      ( ( add @ additive_identity @ A )
      = A ),
    inference(lifteq,[status(thm)],[45]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( multiplicative_identity = B )
      | ( ( add @ A @ ( inverse @ A ) )
       != ( add @ additive_identity @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[32,46]) ).

thf(56,plain,
    ( ( inverse @ additive_identity )
    = multiplicative_identity ),
    inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( additive_identity )),bind(B,$thf( inverse @ additive_identity ))]]) ).

thf(1,negated_conjecture,
    ( ( inverse @ additive_identity )
   != multiplicative_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).

thf(16,plain,
    ( ( inverse @ additive_identity )
   != multiplicative_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(17,plain,
    ( ( inverse @ additive_identity )
   != multiplicative_identity ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(18,plain,
    ( ( inverse @ additive_identity )
   != multiplicative_identity ),
    inference(lifteq,[status(thm)],[17]) ).

thf(65,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[56,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : BOO011-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n007.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sat May 18 14:35:09 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.93/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.04  % [INFO] 	 Parsing done (115ms). 
% 1.27/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.28  % [INFO] 	 nitpick registered as external prover. 
% 1.65/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 1.82/1.35  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 1.95/1.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.95/1.37  % [INFO] 	 Type checking passed. 
% 1.95/1.37  % [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 ... 
% 3.00/1.83  % [INFO] 	 Killing All external provers ... 
% 3.01/1.83  % Time passed: 1256ms (effective reasoning time: 781ms)
% 3.01/1.83  % Axioms used in derivation (2): additive_inverse1, additive_id2
% 3.01/1.83  % No. of inferences in proof: 13
% 3.01/1.83  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1256 ms resp. 781 ms w/o parsing
% 3.01/1.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/1.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------