%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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  : 600s
% DateTime : Sat Jul 16 10:32:13 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;   8 RR)
%            Number of literals    :   17 (   6 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   11 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
    product(X,identity,X) ).

cnf(total_function2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,W)
    | Z = W ) ).

cnf(another_left_identity,hypothesis,
    product(c,A,A) ).

cnf(prove_identity_equals_c,negated_conjecture,
    identity != c ).

cnf(refute_0_0,plain,
    product(c,identity,c),
    inference(subst,[],[right_identity:[bind(X,$fot(c))]]) ).

cnf(refute_0_1,plain,
    product(c,X_11,X_11),
    inference(subst,[],[another_left_identity:[bind(A,$fot(X_11))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(c,X_11,X_11)
    | ~ product(c,X_11,X_8)
    | X_11 = X_8 ),
    inference(subst,[],[total_function2:[bind(W,$fot(X_8)),bind(X,$fot(c)),bind(Y,$fot(X_11)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(c,X_11,X_8)
    | X_11 = X_8 ),
    inference(resolve,[$cnf( product(c,X_11,X_11) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ product(c,identity,c)
    | identity = c ),
    inference(subst,[],[refute_0_3:[bind(X_11,$fot(identity)),bind(X_8,$fot(c))]]) ).

cnf(refute_0_5,plain,
    identity = c,
    inference(resolve,[$cnf( product(c,identity,c) )],[refute_0_0,refute_0_4]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,c) )],[refute_0_5,prove_identity_equals_c]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 23:01:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------