%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT021-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 07:05:38 AM UTC 2025
% Result : Unsatisfiable 14.00s 14.19s
% Output : CNFRefutation 14.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 3 RR)
% Number of literals : 59 ( 58 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 151 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('theBenchmark.p',prove_distributivity) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT004-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT004-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
meet(X,Y) = meet(Y,X),
file('LAT004-0.ax',commutativity_of_meet) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT004-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT004-0.ax',associativity_of_meet) ).
cnf(c6,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT004-0.ax',associativity_of_join) ).
cnf(c7,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c9,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c10,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c11,plain,
meet(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
join(X,join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c17,axiom,
join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)),
file('LAT004-0.ax',quasi_lattice1) ).
cnf(c18,plain,
join(meet(X,Y),meet(X,join(Y,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c19,plain,
join(X,meet(X,join(X,Y))) = meet(X,join(X,Y)),
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c21,axiom,
meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)),
file('LAT004-0.ax',quasi_lattice2) ).
cnf(c22,plain,
meet(join(X,Y),join(X,meet(Y,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c23,plain,
meet(X,join(X,meet(X,Y))) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c24,plain,
meet(X,join(X,meet(Y,X))) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c25,plain,
meet(X,join(X,meet(Y,X))) = join(X,meet(Y,X)),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c30,plain,
join(X,join(Y,meet(X,join(X,Y)))) = join(X,Y),
inference(equational,[status(thm)],[c1,c3,c4,c9,c18]) ).
cnf(c31,plain,
join(X,meet(Y,join(Y,X))) = join(Y,X),
inference(equational,[status(thm)],[c9,c19,c30]) ).
cnf(c32,plain,
join(X,meet(Y,join(X,Y))) = join(Y,X),
inference(equational,[status(thm)],[c4,c31]) ).
cnf(c33,plain,
join(X,meet(Y,join(X,Y))) = join(X,Y),
inference(equational,[status(thm)],[c7,c12,c32]) ).
cnf(c34,plain,
meet(join(X,Y),join(Y,meet(X,Z))) = join(Y,meet(X,Z)),
inference(equational,[status(thm)],[c4,c22]) ).
cnf(c36,plain,
meet(join(X,Y),join(X,meet(Z,Y))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c37,plain,
meet(join(X,Y),join(meet(Y,Z),X)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c4,c22]) ).
cnf(c38,plain,
join(meet(X,Y),meet(join(Y,Z),X)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c39,plain,
join(meet(X,Y),meet(Y,join(X,Z))) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c40,plain,
join(meet(X,Y),meet(X,join(Z,Y))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c42,plain,
join(meet(X,Y),meet(Y,join(Z,X))) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c40]) ).
cnf(c43,plain,
meet(join(X,Y),join(Y,meet(Z,X))) = join(Y,meet(X,Z)),
inference(equational,[status(thm)],[c3,c34]) ).
cnf(c44,plain,
meet(join(X,Y),join(meet(Z,Y),X)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c37]) ).
cnf(c48,plain,
meet(join(X,Y),join(X,meet(Z,Y))) = join(meet(Y,Z),X),
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c49,plain,
meet(join(X,Y),join(X,meet(Z,Y))) = join(X,meet(Z,Y)),
inference(equational,[status(thm)],[c3,c36]) ).
cnf(c50,plain,
join(meet(X,Y),meet(join(X,Z),Y)) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c38]) ).
cnf(c52,plain,
meet(X,meet(join(Y,Z),join(Y,meet(join(Y,Z),X)))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c3,c4,c10,c18,c39,c44,c48,c49]) ).
cnf(c57,plain,
meet(X,meet(join(X,meet(X,Y)),Z)) = meet(join(X,meet(X,Y)),Z),
inference(equational,[status(thm)],[c5,c23]) ).
cnf(c68,plain,
join(meet(X,Y),meet(join(Z,X),Y)) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c50]) ).
cnf(c70,plain,
meet(join(X,Y),join(meet(Z,X),Y)) = join(Y,meet(X,Z)),
inference(equational,[status(thm)],[c4,c44]) ).
cnf(c74,plain,
meet(join(X,Y),join(Y,meet(Z,X))) = join(Y,meet(Z,X)),
inference(equational,[status(thm)],[c4,c49]) ).
cnf(c85,plain,
meet(X,meet(join(Y,Z),join(Y,meet(X,join(Z,Y))))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c3,c4,c10,c40,c42,c70]) ).
cnf(c86,plain,
meet(X,meet(join(X,meet(Y,X)),join(Y,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c10,c12,c18,c25,c38,c48]) ).
cnf(c98,axiom,
join(join(X,meet(Y,Z)),meet(join(X,Y),Z)) = join(X,meet(Y,Z)),
file('theBenchmark.p',bowden) ).
cnf(c99,plain,
join(X,meet(Y,join(Z,X))) = join(X,meet(Z,Y)),
inference(equational,[status(thm)],[c6,c68,c98]) ).
cnf(c101,plain,
join(X,meet(Y,join(X,Z))) = join(X,meet(Z,Y)),
inference(equational,[status(thm)],[c4,c99]) ).
cnf(c102,plain,
join(X,meet(Y,join(Z,X))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c99]) ).
cnf(c104,plain,
join(X,meet(join(X,Y),Z)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c36,c49,c101]) ).
cnf(c105,plain,
meet(X,join(Y,meet(Z,X))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c22,c52,c104]) ).
cnf(c107,plain,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
inference(equational,[status(thm)],[c22,c49,c85,c102,c104]) ).
cnf(c108,plain,
meet(join(X,Y),join(X,Z)) = join(meet(Z,Y),X),
inference(equational,[status(thm)],[c7,c32,c33,c101,c107]) ).
cnf(c110,plain,
meet(X,join(meet(Y,X),Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c11,c40,c42,c105]) ).
cnf(c120,plain,
meet(join(X,Y),join(Z,X)) = join(meet(Z,Y),X),
inference(equational,[status(thm)],[c1,c7,c32,c107,c108]) ).
cnf(c131,plain,
join(meet(X,Y),Z) = meet(join(Y,Z),join(X,Z)),
inference(equational,[status(thm)],[c1,c7,c32,c107,c120]) ).
cnf(c152,plain,
meet(X,meet(join(X,Y),join(Y,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c5,c43,c57,c74,c86,c107]) ).
cnf(c214,plain,
meet(X,meet(Y,meet(join(X,Z),join(W,Z)))) = meet(Y,meet(X,join(W,Z))),
inference(equational,[status(thm)],[c10,c110,c131]) ).
cnf(g1,plain,
meet(a,join(b,c)) = join(meet(a,b),meet(a,c)),
inference(equational,[status(thm)],[c2,c3,c5,c8,c10,c48,c107,c131,c152,c214]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT021-1 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 11:33:04 EDT 2025
% 0.12/0.32 % CPUTime :
% 14.00/14.19 % SZS status Unsatisfiable
% 14.00/14.19 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------