%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP020-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 : Thu Aug 31 00:13:38 EDT 2023

% Result   : Unsatisfiable 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   16 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   16 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    identity: $i ).

tff(decl_23,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_24,type,
    inverse: $i > $i ).

tff(decl_25,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_26,type,
    a: $i ).

cnf(total_function2,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).

cnf(prove_inverse_X_times_X_is_id,negated_conjecture,
    multiply(inverse(a),a) != identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_X_times_X_is_id) ).

cnf(c_0_4,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_5,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_6,plain,
    ( identity = X1
    | ~ product(inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_8,negated_conjecture,
    multiply(inverse(a),a) != identity,
    prove_inverse_X_times_X_is_id ).

cnf(c_0_9,plain,
    multiply(inverse(X1),X1) = identity,
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP020-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n012.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   : Mon Aug 28 23:08:24 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.004000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.007000 s
%------------------------------------------------------------------------------