%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP008-1 : 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 : n013.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 00:13:34 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   23 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :   30 (   5 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  12   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   20 (   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,
    q: $i > $o ).

tff(decl_27,type,
    j: $i > $i ).

tff(decl_28,type,
    h: $i > $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(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).

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

cnf(unknown_meaning3,axiom,
    ( product(j(X1),X1,h(X1))
    | product(X1,j(X1),h(X1))
    | q(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning3) ).

cnf(prove_identity_is_q,negated_conjecture,
    ~ q(identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_q) ).

cnf(unknown_meaning4,axiom,
    ( q(X1)
    | ~ product(j(X1),X1,h(X1))
    | ~ product(X1,j(X1),h(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning4) ).

cnf(c_0_6,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_7,axiom,
    product(X1,identity,X1),
    right_identity ).

cnf(c_0_8,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_9,plain,
    ( X1 = X2
    | ~ product(X2,identity,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    ( product(j(X1),X1,h(X1))
    | product(X1,j(X1),h(X1))
    | q(X1) ),
    unknown_meaning3 ).

cnf(c_0_11,negated_conjecture,
    ~ q(identity),
    prove_identity_is_q ).

cnf(c_0_12,plain,
    ( X1 = X2
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_8]) ).

cnf(c_0_13,axiom,
    ( q(X1)
    | ~ product(j(X1),X1,h(X1))
    | ~ product(X1,j(X1),h(X1)) ),
    unknown_meaning4 ).

cnf(c_0_14,plain,
    h(identity) = j(identity),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]) ).

cnf(c_0_15,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_8]),c_0_7])]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 22:18:16 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.005000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.008000 s
%------------------------------------------------------------------------------