%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL047-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 07:41:29 AM UTC 2025
% Result : Unsatisfiable 109.08s 109.22s
% Output : CNFRefutation 109.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of clauses : 121 ( 121 unt; 0 nHn; 16 RR)
% Number of literals : 121 ( 120 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 200 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(sk1,meet(sk2,sk3)) != meet(sk2,sk3),
file('theBenchmark.p',goals_16) ).
cnf(c1,axiom,
composition(X,one) = X,
file('REL001-0.ax',composition_identity_6) ).
cnf(c2,axiom,
converse(converse(X)) = X,
file('REL001-0.ax',converse_idempotence_8) ).
cnf(c3,axiom,
join(sk1,sk2) = sk2,
file('theBenchmark.p',goals_14) ).
cnf(c4,axiom,
join(sk1,sk3) = sk3,
file('theBenchmark.p',goals_15) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c6,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c7,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c9,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c11,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c13,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c15,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c17,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c19,plain,
join(sk1,join(sk3,X)) = join(sk3,X),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c21,plain,
join(sk1,join(sk2,X)) = join(sk2,X),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c22,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c23,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c24,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c25,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c26,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c25]) ).
cnf(c27,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c28,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c18,c26]) ).
cnf(c29,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c30,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c31,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c30]) ).
cnf(c32,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c7,c9,c31]) ).
cnf(c33,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c5,c31]) ).
cnf(c36,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c31,c32]) ).
cnf(c38,plain,
join(sk1,join(X,sk3)) = join(sk3,X),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c39,plain,
join(sk1,join(X,sk2)) = join(X,sk2),
inference(equational,[status(thm)],[c3,c29]) ).
cnf(c40,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c42,plain,
join(sk3,complement(sk1)) = join(top,sk3),
inference(equational,[status(thm)],[c38,c40]) ).
cnf(c43,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c7,c40]) ).
cnf(c46,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c23,c27]) ).
cnf(c55,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c56,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c55]) ).
cnf(c57,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c26,c27,c56]) ).
cnf(c65,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c31]) ).
cnf(c86,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c9,c31,c33]) ).
cnf(c90,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c7,c15,c31]) ).
cnf(c101,plain,
join(converse(X),composition(converse(Y),Z)) = converse(join(X,composition(converse(Z),Y))),
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c106,plain,
join(sk3,join(complement(sk1),X)) = join(top,join(sk3,X)),
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c111,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c11,c23]) ).
cnf(c112,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c114,plain,
converse(join(X,composition(X,Y))) = converse(composition(X,join(one,Y))),
inference(equational,[status(thm)],[c2,c11,c46,c57,c101]) ).
cnf(c115,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c114]) ).
cnf(c116,plain,
composition(join(one,X),X) = composition(X,join(one,X)),
inference(equational,[status(thm)],[c57,c115]) ).
cnf(c138,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c23,c40]) ).
cnf(c150,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c33,c86]) ).
cnf(c154,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c155,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c5,c154]) ).
cnf(c156,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c26,c28,c155]) ).
cnf(c157,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c32,c156]) ).
cnf(c160,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c7,c40,c156]) ).
cnf(c161,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c43,c160]) ).
cnf(c162,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c5,c161]) ).
cnf(c163,plain,
converse(top) = top,
inference(equational,[status(thm)],[c138,c162]) ).
cnf(c166,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c157]) ).
cnf(c171,plain,
composition(join(one,X),top) = top,
inference(equational,[status(thm)],[c57,c162]) ).
cnf(c172,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c116,c161,c171]) ).
cnf(c173,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c32,c57,c155,c161,c163,c172]) ).
cnf(c187,plain,
join(complement(X),join(Y,complement(X))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c29,c156]) ).
cnf(c223,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c56]) ).
cnf(c224,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c26,c27,c223]) ).
cnf(c232,plain,
join(X,join(Y,composition(Z,X))) = join(composition(join(one,Z),X),Y),
inference(equational,[status(thm)],[c5,c224]) ).
cnf(c250,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c11,c56,c111,c112]) ).
cnf(c251,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c13,c24,c56,c250]) ).
cnf(c252,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c13,c251]) ).
cnf(c256,plain,
composition(complement(X),join(Y,Y)) = composition(complement(X),Y),
inference(equational,[status(thm)],[c156,c252]) ).
cnf(c257,plain,
composition(top,join(X,X)) = composition(top,X),
inference(equational,[status(thm)],[c161,c252]) ).
cnf(c381,plain,
join(X,join(composition(complement(one),X),Y)) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c7,c224]) ).
cnf(c386,plain,
join(X,join(composition(top,X),Y)) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c15,c256,c257,c381]) ).
cnf(c400,plain,
join(X,join(Y,join(complement(join(X,Y)),Z))) = top,
inference(equational,[status(thm)],[c15,c40,c162]) ).
cnf(c401,plain,
join(X,join(sk2,complement(join(X,sk1)))) = top,
inference(equational,[status(thm)],[c5,c39,c400]) ).
cnf(c402,plain,
join(sk2,complement(join(sk1,sk1))) = top,
inference(equational,[status(thm)],[c21,c401]) ).
cnf(c425,plain,
join(X,join(Y,composition(top,X))) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c1,c162,c232,c386]) ).
cnf(c582,axiom,
X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
file('REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c583,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c31,c582]) ).
cnf(c584,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c156,c583]) ).
cnf(c587,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c166,c584]) ).
cnf(c589,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c173,c425,c587]) ).
cnf(c590,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c584,c587]) ).
cnf(c594,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c156,c590]) ).
cnf(c598,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c36,c587,c590]) ).
cnf(c599,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c33,c598]) ).
cnf(c604,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c31,c584,c587]) ).
cnf(c605,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c36,c587,c598,c604]) ).
cnf(c606,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c36,c587,c598,c604]) ).
cnf(c609,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c584,c587,c606]) ).
cnf(c610,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c584,c587,c605]) ).
cnf(c611,plain,
meet(sk1,complement(sk2)) = zero,
inference(equational,[status(thm)],[c32,c33,c402,c594,c610]) ).
cnf(c612,plain,
meet(sk1,sk2) = sk1,
inference(equational,[status(thm)],[c583,c587,c590,c604,c611]) ).
cnf(c621,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c5,c31,c583]) ).
cnf(c632,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c33,c621]) ).
cnf(c634,plain,
join(X,join(X,complement(Y))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c15,c156,c187,c605]) ).
cnf(c639,plain,
join(sk3,complement(meet(sk1,X))) = top,
inference(equational,[status(thm)],[c106,c162,c604]) ).
cnf(c645,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c150,c604]) ).
cnf(c650,plain,
meet(complement(sk3),meet(sk1,X)) = zero,
inference(equational,[status(thm)],[c32,c610,c639]) ).
cnf(c658,plain,
meet(sk3,meet(sk1,X)) = meet(sk1,X),
inference(equational,[status(thm)],[c33,c587,c590,c632,c650]) ).
cnf(c665,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c29,c604]) ).
cnf(c666,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c604,c665]) ).
cnf(c667,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c584,c587,c590,c666]) ).
cnf(c668,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(X,Y)),
inference(equational,[status(thm)],[c33,c667]) ).
cnf(c669,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c33,c667]) ).
cnf(c700,plain,
join(meet(X,Y),complement(meet(Y,X))) = top,
inference(equational,[status(thm)],[c5,c90,c589,c590,c645]) ).
cnf(c812,plain,
complement(join(X,join(complement(Y),Z))) = meet(Y,complement(join(X,Z))),
inference(equational,[status(thm)],[c29,c609]) ).
cnf(c839,plain,
meet(complement(meet(X,Y)),join(complement(X),Y)) = complement(X),
inference(equational,[status(thm)],[c65,c583,c604]) ).
cnf(c840,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c33,c36,c587,c590,c598,c605,c839]) ).
cnf(c1140,plain,
join(X,meet(join(X,Y),complement(join(Y,Z)))) = X,
inference(equational,[status(thm)],[c400,c598,c812,c840]) ).
cnf(c1764,plain,
join(X,meet(complement(Y),meet(Z,join(X,Y)))) = X,
inference(equational,[status(thm)],[c610,c634,c668,c1140]) ).
cnf(c1815,plain,
join(meet(X,Y),meet(Y,meet(Z,X))) = meet(X,Y),
inference(equational,[status(thm)],[c590,c599,c669,c700,c1764]) ).
cnf(c1816,plain,
join(meet(X,sk3),meet(sk1,X)) = meet(X,sk3),
inference(equational,[status(thm)],[c658,c1815]) ).
cnf(c1817,plain,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
inference(equational,[status(thm)],[c5,c612,c1816]) ).
cnf(g1,plain,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
inference(equational,[status(thm)],[c1817]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : REL047-1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 16:20:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 109.08/109.22 % SZS status Unsatisfiable
% 109.08/109.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------