%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Sat Jul 16 10:32:11 EDT 2022

% Result   : Unsatisfiable 1.37s 1.54s
% Output   : CNFRefutation 1.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   22 (  12 unt;   0 nHn;  14 RR)
%            Number of literals    :   41 (   0 equ;  20 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   38 (   2 sgn)

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

cnf(left_identity,axiom,
    product(identity,X,X) ).

cnf(associativity1,axiom,
    ( ~ product(X,Y,U)
    | ~ product(Y,Z,V)
    | ~ product(U,Z,W)
    | product(X,V,W) ) ).

cnf(associativity2,axiom,
    ( ~ product(X,Y,U)
    | ~ product(Y,Z,V)
    | ~ product(X,V,W)
    | product(U,Z,W) ) ).

cnf(prove_there_is_a_right_identity,negated_conjecture,
    ~ product(a,identity,a) ).

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

cnf(refute_0_1,plain,
    ( ~ product(X_35,identity,X_34)
    | ~ product(identity,identity,identity)
    | product(X_34,identity,X_34) ),
    inference(subst,[],[associativity2:[bind(U,$fot(X_34)),bind(V,$fot(identity)),bind(W,$fot(X_34)),bind(X,$fot(X_35)),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(X_35,identity,X_34)
    | product(X_34,identity,X_34) ),
    inference(resolve,[$cnf( product(identity,identity,identity) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ product(inverse(inverse(X_210)),identity,X_210)
    | product(X_210,identity,X_210) ),
    inference(subst,[],[refute_0_2:[bind(X_34,$fot(X_210)),bind(X_35,$fot(inverse(inverse(X_210))))]]) ).

cnf(refute_0_4,plain,
    product(inverse(inverse(X_208)),inverse(X_208),identity),
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_208)))]]) ).

cnf(refute_0_5,plain,
    product(inverse(X_163),X_163,identity),
    inference(subst,[],[left_inverse:[bind(X,$fot(X_163))]]) ).

cnf(refute_0_6,plain,
    product(identity,X_48,X_48),
    inference(subst,[],[left_identity:[bind(X,$fot(X_48))]]) ).

cnf(refute_0_7,plain,
    ( ~ product(X_49,X_50,identity)
    | ~ product(X_50,X_48,X_47)
    | ~ product(identity,X_48,X_48)
    | product(X_49,X_47,X_48) ),
    inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_47)),bind(W,$fot(X_48)),bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(X_48))]]) ).

cnf(refute_0_8,plain,
    ( ~ product(X_49,X_50,identity)
    | ~ product(X_50,X_48,X_47)
    | product(X_49,X_47,X_48) ),
    inference(resolve,[$cnf( product(identity,X_48,X_48) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ product(X_164,inverse(X_163),identity)
    | ~ product(inverse(X_163),X_163,identity)
    | product(X_164,identity,X_163) ),
    inference(subst,[],[refute_0_8:[bind(X_47,$fot(identity)),bind(X_48,$fot(X_163)),bind(X_49,$fot(X_164)),bind(X_50,$fot(inverse(X_163)))]]) ).

cnf(refute_0_10,plain,
    ( ~ product(X_164,inverse(X_163),identity)
    | product(X_164,identity,X_163) ),
    inference(resolve,[$cnf( product(inverse(X_163),X_163,identity) )],[refute_0_5,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ product(inverse(inverse(X_208)),inverse(X_208),identity)
    | product(inverse(inverse(X_208)),identity,X_208) ),
    inference(subst,[],[refute_0_10:[bind(X_163,$fot(X_208)),bind(X_164,$fot(inverse(inverse(X_208))))]]) ).

cnf(refute_0_12,plain,
    product(inverse(inverse(X_208)),identity,X_208),
    inference(resolve,[$cnf( product(inverse(inverse(X_208)),inverse(X_208),identity) )],[refute_0_4,refute_0_11]) ).

cnf(refute_0_13,plain,
    product(inverse(inverse(X_210)),identity,X_210),
    inference(subst,[],[refute_0_12:[bind(X_208,$fot(X_210))]]) ).

cnf(refute_0_14,plain,
    product(X_210,identity,X_210),
    inference(resolve,[$cnf( product(inverse(inverse(X_210)),identity,X_210) )],[refute_0_13,refute_0_3]) ).

cnf(refute_0_15,plain,
    product(a,identity,a),
    inference(subst,[],[refute_0_14:[bind(X_210,$fot(a))]]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( product(a,identity,a) )],[refute_0_15,prove_there_is_a_right_identity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 03:33:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.54  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.54  
% 1.37/1.54  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.37/1.54  
%------------------------------------------------------------------------------