%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 10:32:35 EDT 2022

% Result   : Unsatisfiable 0.46s 0.62s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   20 (  10 unt;   0 nHn;  16 RR)
%            Number of literals    :   35 (   6 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   18 (   1 sgn)

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

cnf(right_inverse,axiom,
    product(X,inverse(X),identity) ).

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

cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ) ).

cnf(another_right_identity,hypothesis,
    ( ~ subgroup_member(A)
    | product(A,another_identity,A) ) ).

cnf(another_identity_in_subgroup,hypothesis,
    subgroup_member(another_identity) ).

cnf(prove_identity_equals_another_identity,negated_conjecture,
    identity != another_identity ).

cnf(refute_0_0,plain,
    product(identity,X_71,X_71),
    inference(subst,[],[left_identity:[bind(X,$fot(X_71))]]) ).

cnf(refute_0_1,plain,
    ( ~ product(identity,X_71,X_71)
    | ~ product(identity,X_71,X_74)
    | X_74 = X_71 ),
    inference(subst,[],[total_function2:[bind(W,$fot(X_71)),bind(X,$fot(identity)),bind(Y,$fot(X_71)),bind(Z,$fot(X_74))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(identity,X_71,X_74)
    | X_74 = X_71 ),
    inference(resolve,[$cnf( product(identity,X_71,X_71) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ product(identity,another_identity,identity)
    | identity = another_identity ),
    inference(subst,[],[refute_0_2:[bind(X_71,$fot(another_identity)),bind(X_74,$fot(identity))]]) ).

cnf(refute_0_4,plain,
    ( ~ subgroup_member(identity)
    | product(identity,another_identity,identity) ),
    inference(subst,[],[another_right_identity:[bind(A,$fot(identity))]]) ).

cnf(refute_0_5,plain,
    product(X_90,inverse(X_90),identity),
    inference(subst,[],[right_inverse:[bind(X,$fot(X_90))]]) ).

cnf(refute_0_6,plain,
    ( ~ product(X_90,inverse(X_90),identity)
    | ~ subgroup_member(X_90)
    | subgroup_member(identity) ),
    inference(subst,[],[closure_of_product_and_inverse:[bind(A,$fot(X_90)),bind(B,$fot(X_90)),bind(C,$fot(identity))]]) ).

cnf(refute_0_7,plain,
    ( ~ subgroup_member(X_90)
    | subgroup_member(identity) ),
    inference(resolve,[$cnf( product(X_90,inverse(X_90),identity) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ subgroup_member(another_identity)
    | subgroup_member(identity) ),
    inference(subst,[],[refute_0_7:[bind(X_90,$fot(another_identity))]]) ).

cnf(refute_0_9,plain,
    subgroup_member(identity),
    inference(resolve,[$cnf( subgroup_member(another_identity) )],[another_identity_in_subgroup,refute_0_8]) ).

cnf(refute_0_10,plain,
    product(identity,another_identity,identity),
    inference(resolve,[$cnf( subgroup_member(identity) )],[refute_0_9,refute_0_4]) ).

cnf(refute_0_11,plain,
    identity = another_identity,
    inference(resolve,[$cnf( product(identity,another_identity,identity) )],[refute_0_10,refute_0_3]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,another_identity) )],[refute_0_11,prove_identity_equals_another_identity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n011.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 17:59:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.62  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.62  
% 0.46/0.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.46/0.63  
%------------------------------------------------------------------------------