%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT038-1 : TPTP v9.0.0. Released v2.4.0.
% 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 07:05:40 AM UTC 2025
% Result : Unsatisfiable 163.83s 163.99s
% Output : CNFRefutation 163.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 12 RR)
% Number of literals : 34 ( 33 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
f(aa,dd) != f(cc,dd),
file('theBenchmark.p',rhs) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT001-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT001-0.ax',idempotence_of_join) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c6,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c7,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c8,axiom,
join(X,meet(X,Y)) = X,
file('LAT001-0.ax',absorption2) ).
cnf(c9,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT001-0.ax',associativity_of_join) ).
cnf(c12,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT001-0.ax',associativity_of_meet) ).
cnf(c13,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c1,c12]) ).
cnf(c14,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c15,axiom,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
file('theBenchmark.p',lhs1) ).
cnf(c16,plain,
f(join(cc,bb),dd) = f(join(aa,bb),dd),
inference(equational,[status(thm)],[c15]) ).
cnf(c21,axiom,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
file('theBenchmark.p',dist_join) ).
cnf(c22,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c21]) ).
cnf(c26,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)),
file('theBenchmark.p',dist_meet) ).
cnf(c27,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c26]) ).
cnf(c28,axiom,
f(join(X,Y),Z) = join(f(X,Z),f(Y,Z)),
file('theBenchmark.p',f_on_left_join) ).
cnf(c29,plain,
join(f(X,Y),f(Z,Y)) = f(join(X,Z),Y),
inference(equational,[status(thm)],[c28]) ).
cnf(c43,plain,
join(meet(X,Y),meet(Y,Z)) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c6,c27]) ).
cnf(c58,plain,
meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c13,c43]) ).
cnf(c63,axiom,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
file('theBenchmark.p',lhs2) ).
cnf(c64,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(aa,dd),f(bb,dd)),
inference(equational,[status(thm)],[c63]) ).
cnf(c81,plain,
meet(f(X,Y),f(join(X,Z),Y)) = f(X,Y),
inference(equational,[status(thm)],[c7,c29]) ).
cnf(c133,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = f(cc,dd),
inference(equational,[status(thm)],[c16,c81]) ).
cnf(c406,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd),
inference(equational,[status(thm)],[c8,c64]) ).
cnf(c407,plain,
meet(f(aa,dd),f(cc,dd)) = f(aa,dd),
inference(equational,[status(thm)],[c16,c29,c58,c81,c406]) ).
cnf(c408,plain,
f(join(aa,cc),dd) = f(cc,dd),
inference(equational,[status(thm)],[c5,c9,c29,c407]) ).
cnf(c610,plain,
meet(join(f(X,Y),Z),f(join(X,W),Y)) = join(f(X,Y),meet(Z,f(W,Y))),
inference(equational,[status(thm)],[c22,c29]) ).
cnf(c929,plain,
join(f(X,Y),meet(Z,f(join(X,W),Y))) = join(f(X,Y),meet(Z,f(W,Y))),
inference(equational,[status(thm)],[c14,c610]) ).
cnf(c930,plain,
f(cc,dd) = f(aa,dd),
inference(equational,[status(thm)],[c8,c29,c64,c133,c408,c929]) ).
cnf(g1,plain,
f(aa,dd) = f(cc,dd),
inference(equational,[status(thm)],[c930]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT038-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.11 % 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 11:34:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 163.83/163.99 % SZS status Unsatisfiable
% 163.83/163.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------