%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 00:13:31 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   26 (  13 unt;   5 typ;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   38 (  20   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   1   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   44 (   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,
    a: $i ).

tff(decl_25,type,
    b: $i ).

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

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).

cnf(square_element,hypothesis,
    product(X1,X1,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_element) ).

cnf(associativity1,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

cnf(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

cnf(a_times_b_is_c,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).

cnf(prove_b_times_a_is_c,negated_conjecture,
    ~ product(b,a,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).

cnf(c_0_7,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_8,hypothesis,
    product(X1,X1,identity),
    square_element ).

cnf(c_0_9,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    associativity1 ).

cnf(c_0_10,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_11,hypothesis,
    ( product(X1,X2,X3)
    | ~ product(X4,identity,X3)
    | ~ product(X4,X2,X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,axiom,
    product(X1,identity,X1),
    right_identity ).

cnf(c_0_13,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,identity)
    | ~ product(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    ( product(X1,X2,X3)
    | ~ product(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,hypothesis,
    product(a,b,c),
    a_times_b_is_c ).

cnf(c_0_16,hypothesis,
    ( product(X1,X2,X3)
    | ~ product(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_17,hypothesis,
    product(c,b,a),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,hypothesis,
    product(c,a,b),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    ~ product(b,a,c),
    prove_b_times_a_is_c ).

cnf(c_0_20,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_18]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n028.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Mon Aug 28 21:32:40 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.006000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.008000 s
%------------------------------------------------------------------------------