%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT032-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 07:05:39 AM UTC 2025
% Result : Unsatisfiable 0.53s 0.70s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 3 RR)
% Number of literals : 13 ( 12 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 26 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)),
file('theBenchmark.p',dist_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT001-0.ax',idempotence_of_join) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c9,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT001-0.ax',associativity_of_meet) ).
cnf(c17,axiom,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
file('theBenchmark.p',dist_join) ).
cnf(c18,plain,
meet(X,meet(join(X,Y),Z)) = meet(X,Z),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c22,plain,
meet(join(X,Y),join(X,Z)) = join(meet(Y,Z),X),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c27,plain,
meet(X,meet(join(Y,X),Z)) = meet(X,Z),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c31,plain,
meet(join(X,Y),join(Z,X)) = join(meet(Y,Z),X),
inference(equational,[status(thm)],[c4,c22]) ).
cnf(c36,plain,
meet(X,join(meet(X,Y),Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c27,c31]) ).
cnf(g1,plain,
meet(xx,join(yy,zz)) = join(meet(xx,yy),meet(xx,zz)),
inference(equational,[status(thm)],[c2,c4,c5,c17,c36]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT032-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n004.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 11:34:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.53/0.70 % SZS status Unsatisfiable
% 0.53/0.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------