%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT028-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 1.08s 1.24s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 3 RR)
% Number of literals : 33 ( 32 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; 2 con; 0-2 aty)
% Number of variables : 68 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(a,b) != meet2(a,b),
file('theBenchmark.p',name) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT005-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT005-0.ax',idempotence_of_join) ).
cnf(c4,axiom,
meet(X,Y) = meet(Y,X),
file('LAT005-0.ax',commutativity_of_meet) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('LAT005-0.ax',commutativity_of_join) ).
cnf(c6,axiom,
meet2(X,Y) = meet2(Y,X),
file('theBenchmark.p',commutativity_of_meet2) ).
cnf(c7,axiom,
meet(meet(join(X,Y),join(Z,Y)),Y) = Y,
file('LAT005-0.ax',wal_1) ).
cnf(c8,plain,
meet(X,meet(join(Y,X),join(Z,X))) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c11,axiom,
join(join(meet(X,Y),meet(Z,Y)),Y) = Y,
file('LAT005-0.ax',wal_2) ).
cnf(c12,plain,
join(X,join(meet(Y,X),meet(Z,X))) = X,
inference(equational,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c14,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c5,c9,c13]) ).
cnf(c16,plain,
meet(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c4,c9,c13]) ).
cnf(c17,plain,
meet(X,meet(X,Y)) = meet(Y,X),
inference(equational,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
join(X,join(X,Y)) = join(Y,X),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c21,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c22,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c23,axiom,
meet2(meet2(join(X,Y),join(Z,Y)),Y) = Y,
file('theBenchmark.p',wal_1_2) ).
cnf(c24,plain,
meet2(X,meet2(join(Y,X),join(Z,X))) = X,
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c29,axiom,
join(join(meet2(X,Y),meet2(Z,Y)),Y) = Y,
file('theBenchmark.p',wal_2_2) ).
cnf(c30,plain,
join(X,join(meet2(Y,X),meet2(Z,X))) = X,
inference(equational,[status(thm)],[c18,c22,c29]) ).
cnf(c31,plain,
join(X,meet2(Y,X)) = X,
inference(equational,[status(thm)],[c2,c30]) ).
cnf(c32,plain,
join(X,meet2(X,Y)) = X,
inference(equational,[status(thm)],[c6,c31]) ).
cnf(c34,plain,
meet(X,meet2(Y,X)) = meet2(Y,X),
inference(equational,[status(thm)],[c9,c17,c21,c31]) ).
cnf(c127,plain,
meet2(meet(X,Y),meet2(Y,join(Z,meet(X,Y)))) = meet(X,Y),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c128,plain,
meet2(meet(X,Y),meet2(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c14,c127]) ).
cnf(c130,plain,
meet(meet(X,Y),meet2(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c17,c21,c34,c128]) ).
cnf(c153,plain,
meet(meet2(X,Y),meet(Y,join(Z,meet2(X,Y)))) = meet2(X,Y),
inference(equational,[status(thm)],[c8,c31]) ).
cnf(c154,plain,
meet2(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c1,c17,c32,c130,c153]) ).
cnf(g1,plain,
meet(a,b) = meet2(a,b),
inference(equational,[status(thm)],[c17,c21,c154]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT028-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n003.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 11:33:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.08/1.24 % SZS status Unsatisfiable
% 1.08/1.24 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------