%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP010-1 : 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 00:13:35 EDT 2023

% Result   : Unsatisfiable 0.14s 0.52s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   30 (  16 unt;   6 typ;   0 def)
%            Number of atoms       :   39 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   32 (  17   ~;  15   |;   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  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (   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 ).

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).

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

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

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

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).

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

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

cnf(c_0_8,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_9,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_10,plain,
    ( product(identity,X1,X2)
    | ~ product(inverse(X3),X4,X2)
    | ~ product(X3,X1,X4) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,axiom,
    product(X1,identity,X1),
    right_identity ).

cnf(c_0_12,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_13,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_14,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_15,plain,
    ( product(identity,X1,inverse(X2))
    | ~ product(X2,X1,identity) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,hypothesis,
    product(a,b,identity),
    a_multiply_b_is_identity ).

cnf(c_0_17,plain,
    ( X1 = X2
    | ~ product(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    ( multiply(X1,X2) = X3
    | ~ product(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

cnf(c_0_19,hypothesis,
    product(identity,b,inverse(a)),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    multiply(identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_21,hypothesis,
    inverse(a) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_22,negated_conjecture,
    ~ product(b,a,identity),
    prove_b_multiply_a_is_identity ).

cnf(c_0_23,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : GRP010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.10  % 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   : Tue Aug 29 02:00:46 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.14/0.51  start to proof: theBenchmark
% 0.14/0.52  % Version  : CSE_E---1.5
% 0.14/0.52  % Problem  : theBenchmark.p
% 0.14/0.52  % Proof found
% 0.14/0.52  % SZS status Theorem for theBenchmark.p
% 0.14/0.52  % SZS output start Proof
% See solution above
% 0.14/0.52  % Total time : 0.004000 s
% 0.14/0.52  % SZS output end Proof
% 0.14/0.52  % Total time : 0.006000 s
%------------------------------------------------------------------------------