%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT241-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 07:05:55 AM UTC 2025
% Result : Unsatisfiable 186.09s 186.12s
% Output : CNFRefutation 186.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 7 RR)
% Number of literals : 35 ( 34 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('theBenchmark.p',prove_distributivity) ).
cnf(c3,axiom,
meet(b,a) = a,
file('theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(c4,axiom,
meet(X,Y) = meet(Y,X),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c6,axiom,
join(X,complement(X)) = one,
file('theBenchmark.p',complement_join) ).
cnf(c7,axiom,
meet(X,complement(X)) = zero,
file('theBenchmark.p',complement_meet) ).
cnf(c8,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c9,axiom,
join(X,meet(X,Y)) = X,
file('theBenchmark.p',absorption2) ).
cnf(c10,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c12,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c14,axiom,
meet(X,join(X,Y)) = X,
file('theBenchmark.p',absorption1) ).
cnf(c15,plain,
meet(X,one) = X,
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c16,plain,
meet(one,X) = X,
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c18,plain,
join(one,X) = one,
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c19,plain,
meet(zero,X) = zero,
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c22,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c24,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c25,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c30,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c4,c25]) ).
cnf(c31,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c34,plain,
meet(X,meet(complement(X),Y)) = zero,
inference(equational,[status(thm)],[c7,c19,c25]) ).
cnf(c35,plain,
join(X,join(complement(X),Y)) = one,
inference(equational,[status(thm)],[c6,c18,c24]) ).
cnf(c36,plain,
meet(b,meet(X,a)) = meet(X,a),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c37,plain,
meet(a,complement(b)) = zero,
inference(equational,[status(thm)],[c4,c34,c36]) ).
cnf(c43,plain,
join(X,join(Y,complement(X))) = one,
inference(equational,[status(thm)],[c5,c35]) ).
cnf(c69,plain,
join(X,join(Y,meet(Z,X))) = join(Y,X),
inference(equational,[status(thm)],[c22,c31]) ).
cnf(c654,axiom,
meet(X,join(Y,meet(Z,join(X,W)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,W)))),
file('theBenchmark.p',equation_H51) ).
cnf(c655,plain,
meet(X,join(Y,join(meet(X,Z),meet(Z,W)))) = meet(X,join(Y,meet(Z,join(X,W)))),
inference(equational,[status(thm)],[c654]) ).
cnf(c661,plain,
meet(X,join(Y,meet(Z,join(X,Y)))) = meet(X,join(meet(X,Z),Y)),
inference(equational,[status(thm)],[c69,c655]) ).
cnf(c662,plain,
meet(X,join(complement(X),meet(X,Y))) = meet(X,join(complement(X),Y)),
inference(equational,[status(thm)],[c5,c6,c15,c661]) ).
cnf(c663,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(equational,[status(thm)],[c5,c7,c10,c37,c662]) ).
cnf(c1310,axiom,
ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y,
file('theBenchmark.p',meet_join_complement) ).
cnf(c1315,plain,
join(complement(b),complement(a)) = complement(a),
inference(equational,[status(thm)],[c8,c43,c663,c1310]) ).
cnf(g1,plain,
join(complement(b),complement(a)) = complement(a),
inference(equational,[status(thm)],[c1315]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : LAT241-10 : TPTP v9.0.0. Released v7.5.0.
% 0.06/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Jul 14 12:02:19 EDT 2025
% 0.10/0.31 % CPUTime :
% 186.09/186.12 % SZS status Unsatisfiable
% 186.09/186.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------