%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP034-3 : 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 : n008.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 00:13:45 EDT 2023

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   20 (  10 unt;   6 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   12 (   1 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,
    subgroup_member: $i > $o ).

tff(decl_27,type,
    a: $i ).

cnf(closure_of_product_and_inverse,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,inverse(X2),X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).

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

cnf(a_is_in_subgroup,hypothesis,
    subgroup_member(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).

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

cnf(prove_a_inverse_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(inverse(a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_in_subgroup) ).

cnf(c_0_5,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,inverse(X2),X3) ),
    closure_of_product_and_inverse ).

cnf(c_0_6,axiom,
    product(X1,inverse(X1),identity),
    right_inverse ).

cnf(c_0_7,plain,
    ( subgroup_member(identity)
    | ~ subgroup_member(X1) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_8,hypothesis,
    subgroup_member(a),
    a_is_in_subgroup ).

cnf(c_0_9,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_10,hypothesis,
    subgroup_member(identity),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_10])]) ).

cnf(c_0_12,negated_conjecture,
    ~ subgroup_member(inverse(a)),
    prove_a_inverse_is_in_subgroup ).

cnf(c_0_13,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP034-3 : 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
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 29 00:02:02 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.58  % Version  : CSE_E---1.5
% 0.21/0.58  % Problem  : theBenchmark.p
% 0.21/0.58  % Proof found
% 0.21/0.58  % SZS status Theorem for theBenchmark.p
% 0.21/0.58  % SZS output start Proof
% See solution above
% 0.21/0.58  % Total time : 0.004000 s
% 0.21/0.58  % SZS output end Proof
% 0.21/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------