%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT013-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 : 300s
% DateTime : Tue Jul 15 07:05:37 AM UTC 2025
% Result : Unsatisfiable 7.43s 7.60s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 3 RR)
% Number of literals : 47 ( 46 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('theBenchmark.p',prove_associativity_of_meet) ).
cnf(c1,axiom,
join(X,meet(Y,meet(X,Z))) = X,
file('theBenchmark.p',mckenzie1) ).
cnf(c2,axiom,
meet(X,join(Y,join(X,Z))) = X,
file('theBenchmark.p',mckenzie2) ).
cnf(c3,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,axiom,
join(join(meet(X,Y),meet(Y,Z)),Y) = Y,
file('theBenchmark.p',mckenzie3) ).
cnf(c8,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c10,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c11,plain,
join(meet(X,Y),Y) = Y,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c12,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c14,plain,
join(join(X,Y),X) = join(X,Y),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c15,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c16,plain,
join(meet(X,Y),X) = X,
inference(equational,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
meet(meet(X,Y),X) = meet(X,Y),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c21,plain,
join(meet(X,meet(Y,Z)),Y) = Y,
inference(equational,[status(thm)],[c1,c12]) ).
cnf(c22,axiom,
meet(meet(join(X,Y),join(Y,Z)),Y) = Y,
file('theBenchmark.p',mckenzie4) ).
cnf(c23,plain,
meet(join(X,Y),Y) = Y,
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c27,plain,
join(join(X,Y),meet(Z,Y)) = join(X,Y),
inference(equational,[status(thm)],[c1,c23]) ).
cnf(c28,plain,
join(X,meet(Y,meet(Z,X))) = X,
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c31,plain,
meet(X,meet(Y,meet(X,Z))) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c1,c23]) ).
cnf(c32,plain,
meet(meet(X,meet(Y,Z)),Y) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c37,plain,
join(join(X,Y),meet(Z,X)) = join(X,Y),
inference(equational,[status(thm)],[c14,c27]) ).
cnf(c54,plain,
join(meet(meet(X,Y),Z),X) = X,
inference(equational,[status(thm)],[c17,c21]) ).
cnf(c56,plain,
join(X,meet(meet(Y,X),Z)) = X,
inference(equational,[status(thm)],[c17,c28]) ).
cnf(c57,plain,
join(X,meet(meet(X,Y),Z)) = X,
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c62,plain,
join(join(X,Y),meet(X,Z)) = join(X,Y),
inference(equational,[status(thm)],[c17,c37]) ).
cnf(c74,plain,
meet(meet(meet(X,Y),Z),X) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c17,c32]) ).
cnf(c194,plain,
meet(meet(X,join(meet(Y,X),Z)),meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c195,plain,
meet(meet(X,Y),meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c16,c194]) ).
cnf(c196,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c17,c195]) ).
cnf(c280,plain,
meet(meet(X,Y),meet(Y,join(Z,meet(X,Y)))) = meet(X,Y),
inference(equational,[status(thm)],[c12,c194,c196]) ).
cnf(c281,plain,
meet(meet(X,Y),meet(Y,join(X,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c62,c280]) ).
cnf(c319,plain,
meet(meet(X,Y),meet(Z,meet(Y,X))) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c31,c195]) ).
cnf(c330,plain,
meet(meet(meet(X,Y),Z),meet(Z,X)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c57,c280]) ).
cnf(c331,plain,
meet(meet(meet(X,Y),Z),meet(Z,Y)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c56,c280]) ).
cnf(c332,plain,
meet(meet(X,Y),meet(meet(Y,Z),X)) = meet(meet(Y,Z),X),
inference(equational,[status(thm)],[c54,c194]) ).
cnf(c334,plain,
meet(X,meet(Y,join(X,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c196,c281,c330,c332]) ).
cnf(c335,plain,
meet(meet(X,Y),meet(Y,Z)) = meet(meet(Y,Z),X),
inference(equational,[status(thm)],[c330,c332]) ).
cnf(c336,plain,
meet(meet(X,Y),meet(Z,Y)) = meet(meet(Z,Y),X),
inference(equational,[status(thm)],[c330,c331,c332]) ).
cnf(c339,plain,
meet(meet(X,Y),meet(Y,Z)) = meet(meet(Z,Y),X),
inference(equational,[status(thm)],[c196,c336]) ).
cnf(c340,plain,
meet(meet(X,Y),meet(Z,X)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c196,c335]) ).
cnf(c341,plain,
meet(meet(X,Y),meet(Z,Y)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c11,c334]) ).
cnf(c343,plain,
meet(meet(X,Y),Z) = meet(meet(Z,X),Y),
inference(equational,[status(thm)],[c319,c340,c341]) ).
cnf(c345,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c196,c343]) ).
cnf(c346,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c74,c339,c343,c345]) ).
cnf(g1,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(equational,[status(thm)],[c196,c346]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT013-1 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 11:32:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 7.43/7.60 % SZS status Unsatisfiable
% 7.43/7.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------