%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP013-1 : 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 : n032.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 00:13:37 EDT 2023

% Result   : Unsatisfiable 0.14s 0.48s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (  17 unt;   8 typ;   0 def)
%            Number of atoms       :   31 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   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  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   25 (   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 ).

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

tff(decl_28,type,
    c: $i ).

tff(decl_29,type,
    d: $i ).

cnf(total_function2,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).

cnf(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).

cnf(inverses_have_property,hypothesis,
    ( product(X1,X3,X2)
    | ~ product(inverse(X1),inverse(X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverses_have_property) ).

cnf(right_inverse,axiom,
    product(X1,inverse(X1),identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).

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

cnf(inverse_a_times_inverse_b_is_d,hypothesis,
    product(inverse(a),inverse(b),d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_a_times_inverse_b_is_d) ).

cnf(prove_c_times_d_is_identity,negated_conjecture,
    ~ product(c,d,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_times_d_is_identity) ).

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

cnf(c_0_8,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

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

cnf(c_0_10,hypothesis,
    ( product(X1,X3,X2)
    | ~ product(inverse(X1),inverse(X2),X3) ),
    inverses_have_property ).

cnf(c_0_11,axiom,
    product(X1,inverse(X1),identity),
    right_inverse ).

cnf(c_0_12,plain,
    ( X1 = X2
    | ~ product(X1,identity,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,hypothesis,
    product(X1,identity,inverse(X1)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,hypothesis,
    product(a,b,c),
    a_times_b_is_c ).

cnf(c_0_15,hypothesis,
    product(inverse(a),inverse(b),d),
    inverse_a_times_inverse_b_is_d ).

cnf(c_0_16,hypothesis,
    inverse(X1) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,hypothesis,
    ( c = X1
    | ~ product(a,b,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_14]) ).

cnf(c_0_18,hypothesis,
    product(a,b,d),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ~ product(c,d,identity),
    prove_c_times_d_is_identity ).

cnf(c_0_20,hypothesis,
    d = c,
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,hypothesis,
    product(X1,X1,identity),
    squareness ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09  % Problem    : GRP013-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Mon Aug 28 21:07:01 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.14/0.46  start to proof: theBenchmark
% 0.14/0.48  % Version  : CSE_E---1.5
% 0.14/0.48  % Problem  : theBenchmark.p
% 0.14/0.48  % Proof found
% 0.14/0.48  % SZS status Theorem for theBenchmark.p
% 0.14/0.48  % SZS output start Proof
% See solution above
% 0.14/0.48  % Total time : 0.003000 s
% 0.14/0.48  % SZS output end Proof
% 0.14/0.48  % Total time : 0.006000 s
%------------------------------------------------------------------------------