%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP586-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 : Fri May 19 11:14:27 EDT 2023

% Result   : Unsatisfiable 2.58s 1.58s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   12 (   7 unt;   5 typ;   0 def)
%            Number of atoms       :    7 (   6 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   44 (   2   ~;   0   |;   0   &;  42   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   0   ^;  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(multiply_type,type,
    multiply: $i > $i > $i ).

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

thf(b2_type,type,
    b2: $i ).

thf(a2_type,type,
    a2: $i ).

thf(double_divide_type,type,
    double_divide: $i > $i > $i ).

thf(1,negated_conjecture,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

thf(4,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( double_divide @ A @ ( inverse @ ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ C ) ) ) @ B ) ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

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

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( inverse @ ( double_divide @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

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

thf(17,plain,
    $false,
    inference(e,[status(thm)],[4,7,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP586-1 : TPTP v8.1.2. Released v2.6.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May 19 01:21:47 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 1.00/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.22/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.24  % [INFO] 	 Found a conjecture and 2 axioms. Running axiom selection ... 
% 1.84/1.26  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.84/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.84/1.27  % [INFO] 	 Type checking passed. 
% 1.84/1.27  % [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 ... 
% 2.58/1.57  % External prover 'e' found a proof!
% 2.58/1.57  % [INFO] 	 Killing All external provers ... 
% 2.58/1.57  % Time passed: 1064ms (effective reasoning time: 579ms)
% 2.58/1.57  % 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)>
% 2.58/1.57  % Axioms used in derivation (2): single_axiom, multiply
% 2.58/1.57  % No. of inferences in proof: 7
% 2.58/1.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1064 ms resp. 579 ms w/o parsing
% 2.84/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.84/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------