%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP014-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 11:13:00 EDT 2023

% Result   : Unsatisfiable 3.68s 1.79s
% Output   : Refutation 3.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   10 (   5 unt;   5 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 :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^;   8   !;   0   ?;   8   :)

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

thf(a_type,type,
    a: $i ).

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

thf(c_type,type,
    c: $i ).

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

thf(1,negated_conjecture,
    ( ( multiply @ a @ ( multiply @ b @ c ) )
   != ( multiply @ ( multiply @ a @ b ) @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).

thf(3,plain,
    ( ( multiply @ a @ ( multiply @ b @ c ) )
   != ( multiply @ ( multiply @ a @ b ) @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

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

thf(36,plain,
    $false,
    inference(e,[status(thm)],[3,6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n002.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 02:09:20 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.93/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.00  % [INFO] 	 Parsing done (112ms). 
% 1.24/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.56/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.56/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.56/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.25  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ... 
% 1.75/1.26  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.86/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.86/1.27  % [INFO] 	 Type checking passed. 
% 1.86/1.28  % [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 ... 
% 3.68/1.79  % External prover 'e' found a proof!
% 3.68/1.79  % [INFO] 	 Killing All external provers ... 
% 3.68/1.79  % Time passed: 1258ms (effective reasoning time: 780ms)
% 3.68/1.79  % 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)>
% 3.68/1.79  % Axioms used in derivation (1): group_axiom
% 3.68/1.79  % No. of inferences in proof: 5
% 3.68/1.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1258 ms resp. 780 ms w/o parsing
% 3.68/1.81  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.68/1.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------