%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP028-4 : TPTP v8.1.0. Released v2.6.0.
% 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 10:32:32 EDT 2022

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% 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(associativity1,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_29,X_29)),right_solution(X_29,X_29),not_identity(right_solution(X_29,X_29))),
    inference(subst,[],[prove_there_is_a_right_identity:[bind(X,$fot(right_solution(X_29,X_29)))]]) ).

cnf(refute_0_1,plain,
    product(X_26,right_solution(X_26,X_26),X_26),
    inference(subst,[],[right_soln:[bind(X,$fot(X_26)),bind(Y,$fot(X_26))]]) ).

cnf(refute_0_2,plain,
    product(left_solution(X_23,X_21),X_23,X_21),
    inference(subst,[],[left_soln:[bind(X,$fot(X_23)),bind(Y,$fot(X_21))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_23,X_24,X_23)
    | ~ product(left_solution(X_23,X_21),X_23,X_21)
    | product(X_21,X_24,X_21) ),
    inference(subst,[],[associativity1:[bind(U,$fot(X_21)),bind(V,$fot(X_23)),bind(W,$fot(X_21)),bind(X,$fot(left_solution(X_23,X_21))),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_4,plain,
    ( ~ product(X_23,X_24,X_23)
    | product(X_21,X_24,X_21) ),
    inference(resolve,[$cnf( product(left_solution(X_23,X_21),X_23,X_21) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ product(X_26,right_solution(X_26,X_26),X_26)
    | product(X_25,right_solution(X_26,X_26),X_25) ),
    inference(subst,[],[refute_0_4:[bind(X_21,$fot(X_25)),bind(X_23,$fot(X_26)),bind(X_24,$fot(right_solution(X_26,X_26)))]]) ).

cnf(refute_0_6,plain,
    product(X_25,right_solution(X_26,X_26),X_25),
    inference(resolve,[$cnf( product(X_26,right_solution(X_26,X_26),X_26) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    product(not_identity(right_solution(X_29,X_29)),right_solution(X_29,X_29),not_identity(right_solution(X_29,X_29))),
    inference(subst,[],[refute_0_6:[bind(X_25,$fot(not_identity(right_solution(X_29,X_29)))),bind(X_26,$fot(X_29))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( product(not_identity(right_solution(X_29,X_29)),right_solution(X_29,X_29),not_identity(right_solution(X_29,X_29))) )],[refute_0_7,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP028-4 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 13:23:07 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------