%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL006-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 07:41:16 AM UTC 2025
% Result : Unsatisfiable 64.57s 64.70s
% Output : CNFRefutation 64.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 18 RR)
% Number of literals : 97 ( 96 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(sk1,converse(sk2)) != zero,
file('theBenchmark.p',goals_15) ).
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(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c4,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c5,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c7,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
meet(converse(sk1),sk2) = zero,
file('theBenchmark.p',goals_14) ).
cnf(c9,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c10,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c12,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c14,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c16,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c18,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c19,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c20,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c21,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c22,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c21]) ).
cnf(c23,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c24,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c17,c22]) ).
cnf(c25,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c26,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c27,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c26]) ).
cnf(c28,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c5,c7,c27]) ).
cnf(c29,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c30,plain,
join(top,zero) = top,
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c32,plain,
meet(sk2,converse(sk1)) = zero,
inference(equational,[status(thm)],[c8,c29]) ).
cnf(c33,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c27,c28]) ).
cnf(c35,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c36,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c5,c35]) ).
cnf(c38,plain,
join(top,join(zero,X)) = join(top,X),
inference(equational,[status(thm)],[c28,c35]) ).
cnf(c40,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c3,c38]) ).
cnf(c42,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c25]) ).
cnf(c43,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c44,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c43]) ).
cnf(c54,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c27]) ).
cnf(c63,plain,
converse(join(X,join(converse(Y),Z))) = join(Y,converse(join(X,Z))),
inference(equational,[status(thm)],[c19,c25]) ).
cnf(c70,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c7,c27,c29]) ).
cnf(c75,plain,
meet(top,join(complement(X),complement(Y))) = complement(join(zero,meet(X,Y))),
inference(equational,[status(thm)],[c28,c54]) ).
cnf(c78,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c79,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c104,plain,
join(top,join(X,join(zero,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c25,c38]) ).
cnf(c110,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c19,c35]) ).
cnf(c119,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c29,c70]) ).
cnf(c123,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c124,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c123]) ).
cnf(c125,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c22,c24,c124]) ).
cnf(c126,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c28,c125]) ).
cnf(c129,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c42,c125]) ).
cnf(c130,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c36,c129]) ).
cnf(c132,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c30,c40,c104,c126,c130]) ).
cnf(c133,plain,
converse(top) = top,
inference(equational,[status(thm)],[c110,c132]) ).
cnf(c136,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c16,c126]) ).
cnf(c179,plain,
join(X,join(converse(complement(converse(X))),Y)) = top,
inference(equational,[status(thm)],[c18,c110,c132,c133]) ).
cnf(c181,plain,
join(complement(converse(X)),converse(join(X,Y))) = top,
inference(equational,[status(thm)],[c63,c133,c179]) ).
cnf(c191,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c16,c44]) ).
cnf(c193,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c22,c23,c25,c191]) ).
cnf(c199,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c24,c193]) ).
cnf(c209,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c10,c44,c78,c79]) ).
cnf(c210,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c12,c20,c44,c209]) ).
cnf(c211,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c12,c210]) ).
cnf(c215,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c125,c211]) ).
cnf(c234,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c27,c215]) ).
cnf(c468,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(c469,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c27,c468]) ).
cnf(c470,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c125,c469]) ).
cnf(c473,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c136,c470]) ).
cnf(c475,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c470,c473]) ).
cnf(c476,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c473]) ).
cnf(c481,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c33,c473,c475]) ).
cnf(c482,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c29,c481]) ).
cnf(c483,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c24,c199,c234,c469]) ).
cnf(c486,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c27,c470,c473]) ).
cnf(c488,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c33,c473,c481,c486]) ).
cnf(c499,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c29,c483]) ).
cnf(c500,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c27,c469]) ).
cnf(c504,plain,
meet(sk2,complement(converse(sk1))) = sk2,
inference(equational,[status(thm)],[c32,c473,c500]) ).
cnf(c505,plain,
join(converse(sk1),complement(sk2)) = complement(sk2),
inference(equational,[status(thm)],[c3,c488,c504]) ).
cnf(c522,plain,
join(complement(sk1),converse(complement(sk2))) = top,
inference(equational,[status(thm)],[c2,c181,c505]) ).
cnf(c529,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c119,c486]) ).
cnf(c532,plain,
join(complement(X),join(complement(Y),Z)) = join(complement(meet(X,Y)),Z),
inference(equational,[status(thm)],[c16,c486]) ).
cnf(c533,plain,
complement(meet(meet(X,Y),Z)) = complement(meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c486,c532]) ).
cnf(c534,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c470,c473,c475,c533]) ).
cnf(c535,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c29,c534]) ).
cnf(c538,plain,
join(complement(sk2),converse(complement(sk1))) = top,
inference(equational,[status(thm)],[c3,c18,c133,c522]) ).
cnf(c539,plain,
meet(sk2,converse(complement(sk1))) = sk2,
inference(equational,[status(thm)],[c28,c469,c476,c538]) ).
cnf(c542,plain,
meet(X,meet(Y,complement(meet(X,Y)))) = zero,
inference(equational,[status(thm)],[c29,c75,c473,c475,c482,c486,c529,c535]) ).
cnf(c567,plain,
join(sk2,converse(complement(sk1))) = converse(complement(sk1)),
inference(equational,[status(thm)],[c3,c499,c539]) ).
cnf(c571,plain,
complement(meet(sk1,converse(sk2))) = top,
inference(equational,[status(thm)],[c2,c29,c181,c486,c567]) ).
cnf(c572,plain,
meet(sk1,converse(sk2)) = zero,
inference(equational,[status(thm)],[c482,c542,c571]) ).
cnf(g1,plain,
meet(sk1,converse(sk2)) = zero,
inference(equational,[status(thm)],[c572]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : REL006-1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n002.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 16:07:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 64.57/64.70 % SZS status Unsatisfiable
% 64.57/64.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------