%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : GRP418-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n029.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 07:06:41 EDT 2024

% Result   : Unsatisfiable 8.60s 3.74s
% Output   : Refutation 8.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :    5 (   4 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   52 (   2   ~;   0   |;   0   &;  50   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 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   :    6 (   0   ^   6   !;   0   ?;   6   :)

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

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

thf(a1_type,type,
    a1: $i ).

thf(b1_type,type,
    b1: $i ).

thf(1,negated_conjecture,
    ( ( multiply @ ( inverse @ a1 ) @ a1 )
   != ( multiply @ ( inverse @ b1 ) @ b1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).

thf(3,plain,
    ( ( multiply @ ( inverse @ a1 ) @ a1 )
   != ( multiply @ ( inverse @ b1 ) @ b1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ B ) @ ( inverse @ ( multiply @ C @ ( inverse @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) ) ) ) @ ( multiply @ A @ C ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(153,plain,
    $false,
    inference(e,[status(thm)],[3,6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP418-1 : TPTP v8.2.0. Released v2.6.0.
% 0.00/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Jun 20 12:26:55 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.96/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (94ms). 
% 1.19/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.83/1.24  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.83/1.25  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.83/1.25  % [INFO] 	 Type checking passed. 
% 1.83/1.26  % [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 ... 
% 8.60/3.73  % External prover 'e' found a proof!
% 8.60/3.73  % [INFO] 	 Killing All external provers ... 
% 8.60/3.73  % Time passed: 3208ms (effective reasoning time: 2766ms)
% 8.60/3.74  % Axioms used in derivation (1): single_axiom
% 8.60/3.74  % No. of inferences in proof: 5
% 8.60/3.74  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3208 ms resp. 2766 ms w/o parsing
% 8.60/3.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.60/3.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------