%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT011-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 1.74s 1.95s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 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 : 52 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(a,b) != meet2(a,b),
file('theBenchmark.p',prove_meets_are_same) ).
cnf(c4,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c6,axiom,
meet2(X,Y) = meet2(Y,X),
file('theBenchmark.p',commutativity_of_meet2) ).
cnf(c7,axiom,
meet2(X,join(X,Y)) = X,
file('theBenchmark.p',absorption1_2) ).
cnf(c8,axiom,
join(X,meet2(X,Y)) = X,
file('theBenchmark.p',absorption2_2) ).
cnf(c9,axiom,
join(X,meet(X,Y)) = X,
file('LAT001-0.ax',absorption2) ).
cnf(c10,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c11,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c12,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c13,plain,
join(X,meet2(Y,X)) = X,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c14,plain,
meet2(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c15,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT001-0.ax',associativity_of_meet) ).
cnf(c16,axiom,
meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)),
file('theBenchmark.p',associativity_of_meet2) ).
cnf(c25,plain,
meet(X,meet2(Y,X)) = meet2(Y,X),
inference(equational,[status(thm)],[c4,c11,c13]) ).
cnf(c27,plain,
meet(X,meet2(X,Y)) = meet2(X,Y),
inference(equational,[status(thm)],[c4,c8,c11]) ).
cnf(c29,plain,
meet2(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c6,c12,c14]) ).
cnf(c30,plain,
meet2(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c6,c9,c14]) ).
cnf(c117,plain,
join(meet(X,Y),meet(X,meet(Y,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c121,plain,
meet2(X,meet2(Y,join(meet2(X,Y),Z))) = meet2(X,Y),
inference(equational,[status(thm)],[c7,c16]) ).
cnf(c154,plain,
meet2(X,meet2(Y,join(Z,meet2(X,Y)))) = meet2(X,Y),
inference(equational,[status(thm)],[c5,c121]) ).
cnf(c219,plain,
join(meet(X,Y),meet(X,meet2(Y,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c27,c117]) ).
cnf(c220,plain,
join(meet(X,Y),meet2(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c25,c219]) ).
cnf(c221,plain,
meet2(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c29,c30,c154,c220]) ).
cnf(g1,plain,
meet(a,b) = meet2(a,b),
inference(equational,[status(thm)],[c4,c221]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT011-1 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 11:32:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.74/1.95 % SZS status Unsatisfiable
% 1.74/1.95 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------