%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP028-3 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   13 (   9 unt;   0 nHn;   5 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 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity2,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_73,X_73)),right_solution(X_73,X_73),not_identity(right_solution(X_73,X_73))),
    inference(subst,[],[prove_there_is_a_right_identity:[bind(X,$fot(right_solution(X_73,X_73)))]]) ).

cnf(refute_0_1,plain,
    product(X_70,right_solution(X_70,X_70),X_70),
    inference(subst,[],[right_soln:[bind(X,$fot(X_70)),bind(Y,$fot(X_70))]]) ).

cnf(refute_0_2,plain,
    product(left_solution(X_67,X_65),X_67,X_65),
    inference(subst,[],[left_soln:[bind(X,$fot(X_67)),bind(Y,$fot(X_65))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_67,X_68,X_67)
    | ~ product(left_solution(X_67,X_65),X_67,X_65)
    | product(X_65,X_68,X_65) ),
    inference(subst,[],[associativity2:[bind(U,$fot(X_65)),bind(V,$fot(X_67)),bind(W,$fot(X_65)),bind(X,$fot(left_solution(X_67,X_65))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_67,X_68,X_67)
    | product(X_65,X_68,X_65) ),
    inference(resolve,[$cnf( product(left_solution(X_67,X_65),X_67,X_65) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ product(X_70,right_solution(X_70,X_70),X_70)
    | product(X_69,right_solution(X_70,X_70),X_69) ),
    inference(subst,[],[refute_0_4:[bind(X_65,$fot(X_69)),bind(X_67,$fot(X_70)),bind(X_68,$fot(right_solution(X_70,X_70)))]]) ).

cnf(refute_0_6,plain,
    product(X_69,right_solution(X_70,X_70),X_69),
    inference(resolve,[$cnf( product(X_70,right_solution(X_70,X_70),X_70) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    product(not_identity(right_solution(X_73,X_73)),right_solution(X_73,X_73),not_identity(right_solution(X_73,X_73))),
    inference(subst,[],[refute_0_6:[bind(X_69,$fot(not_identity(right_solution(X_73,X_73)))),bind(X_70,$fot(X_73))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( product(not_identity(right_solution(X_73,X_73)),right_solution(X_73,X_73),not_identity(right_solution(X_73,X_73))) )],[refute_0_7,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP028-3 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n027.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 : Mon Jun 13 04:58:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37  
% 0.12/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38  
%------------------------------------------------------------------------------