%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP028-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 10:32:32 EDT 2022

% Result   : Unsatisfiable 0.15s 0.37s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   13 (   9 unt;   0 nHn;   7 RR)
%            Number of literals    :   20 (   0 equ;   9 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;   0 con; 1-2 aty)
%            Number of variables   :   26 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity,axiom,
    ( ~ product(X,Y,U)
    | ~ product(Y,Z,V)
    | ~ product(X,V,W)
    | product(U,Z,W) ) ).

cnf(left_soln,hypothesis,
    product(left_solution(X,Y),X,Y) ).

cnf(right_soln,hypothesis,
    product(X,right_solution(X,Y),Y) ).

cnf(prove_there_is_a_right_identity,negated_conjecture,
    ~ product(not_identity(X),X,not_identity(X)) ).

cnf(refute_0_0,plain,
    ~ product(not_identity(right_solution(X_21,X_21)),right_solution(X_21,X_21),not_identity(right_solution(X_21,X_21))),
    inference(subst,[],[prove_there_is_a_right_identity:[bind(X,$fot(right_solution(X_21,X_21)))]]) ).

cnf(refute_0_1,plain,
    product(left_solution(X_19,X_17),X_19,X_17),
    inference(subst,[],[left_soln:[bind(X,$fot(X_19)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_2,plain,
    product(X_15,right_solution(X_15,X_15),X_15),
    inference(subst,[],[right_soln:[bind(X,$fot(X_15)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_14,X_15,X_13)
    | ~ product(X_15,right_solution(X_15,X_15),X_15)
    | product(X_13,right_solution(X_15,X_15),X_13) ),
    inference(subst,[],[associativity:[bind(U,$fot(X_13)),bind(V,$fot(X_15)),bind(W,$fot(X_13)),bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(right_solution(X_15,X_15)))]]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_14,X_15,X_13)
    | product(X_13,right_solution(X_15,X_15),X_13) ),
    inference(resolve,[$cnf( product(X_15,right_solution(X_15,X_15),X_15) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ product(left_solution(X_19,X_17),X_19,X_17)
    | product(X_17,right_solution(X_19,X_19),X_17) ),
    inference(subst,[],[refute_0_4:[bind(X_13,$fot(X_17)),bind(X_14,$fot(left_solution(X_19,X_17))),bind(X_15,$fot(X_19))]]) ).

cnf(refute_0_6,plain,
    product(X_17,right_solution(X_19,X_19),X_17),
    inference(resolve,[$cnf( product(left_solution(X_19,X_17),X_19,X_17) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    product(not_identity(right_solution(X_21,X_21)),right_solution(X_21,X_21),not_identity(right_solution(X_21,X_21))),
    inference(subst,[],[refute_0_6:[bind(X_17,$fot(not_identity(right_solution(X_21,X_21)))),bind(X_19,$fot(X_21))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( product(not_identity(right_solution(X_21,X_21)),right_solution(X_21,X_21),not_identity(right_solution(X_21,X_21))) )],[refute_0_7,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP028-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15  % Command  : metis --show proof --show saturation %s
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Tue Jun 14 11:47:28 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37  
% 0.15/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.38  
%------------------------------------------------------------------------------