%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL050-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 07:41:30 AM UTC 2025
% Result : Unsatisfiable 123.92s 124.22s
% Output : CNFRefutation 123.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of clauses : 133 ( 133 unt; 0 nHn; 14 RR)
% Number of literals : 133 ( 132 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 209 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('theBenchmark.p',goals_14) ).
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,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c9,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c11,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c13,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
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,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c17,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c18,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c19,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c20,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c21,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c20]) ).
cnf(c22,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c23,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c21]) ).
cnf(c24,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c25,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c26,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c25]) ).
cnf(c27,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c5,c7,c26]) ).
cnf(c28,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c31,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c26,c27]) ).
cnf(c33,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c34,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c5,c33]) ).
cnf(c37,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c11,c22]) ).
cnf(c39,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c42,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c44,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c45,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c44]) ).
cnf(c46,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c21,c22,c45]) ).
cnf(c48,plain,
join(X,X) = composition(join(one,one),X),
inference(equational,[status(thm)],[c23,c46]) ).
cnf(c52,plain,
composition(converse(X),composition(converse(Y),Z)) = composition(converse(composition(Y,X)),Z),
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c53,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c11,c15]) ).
cnf(c55,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c26]) ).
cnf(c70,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c5,c15,c26]) ).
cnf(c71,plain,
join(zero,join(complement(X),meet(X,top))) = top,
inference(equational,[status(thm)],[c24,c27,c70]) ).
cnf(c72,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c27,c71]) ).
cnf(c74,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c7,c26,c28]) ).
cnf(c86,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c9,c17]) ).
cnf(c88,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c91,plain,
join(X,composition(X,converse(Y))) = composition(X,converse(join(one,Y))),
inference(equational,[status(thm)],[c18,c19,c46]) ).
cnf(c92,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c37,c91]) ).
cnf(c93,plain,
composition(join(one,X),X) = composition(X,join(one,X)),
inference(equational,[status(thm)],[c46,c92]) ).
cnf(c114,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c116,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c3,c5,c53]) ).
cnf(c117,plain,
join(complement(X),join(Y,X)) = join(top,Y),
inference(equational,[status(thm)],[c2,c11,c116]) ).
cnf(c124,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c28,c74]) ).
cnf(c126,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c127,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c126]) ).
cnf(c128,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c21,c23,c127]) ).
cnf(c129,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c27,c128]) ).
cnf(c130,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c26,c128]) ).
cnf(c131,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c27,c130]) ).
cnf(c132,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c42,c128]) ).
cnf(c133,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c34,c132]) ).
cnf(c134,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c3,c133]) ).
cnf(c135,plain,
converse(top) = top,
inference(equational,[status(thm)],[c114,c134]) ).
cnf(c137,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c129]) ).
cnf(c140,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(equational,[status(thm)],[c1,c127]) ).
cnf(c143,plain,
composition(join(one,X),top) = top,
inference(equational,[status(thm)],[c46,c134]) ).
cnf(c144,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c93,c133,c143]) ).
cnf(c145,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c27,c46,c127,c133,c135,c144]) ).
cnf(c148,plain,
join(complement(one),composition(X,complement(converse(X)))) = complement(one),
inference(equational,[status(thm)],[c2,c140]) ).
cnf(c151,plain,
composition(top,converse(X)) = converse(composition(X,top)),
inference(equational,[status(thm)],[c19,c135]) ).
cnf(c167,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(equational,[status(thm)],[c27,c127]) ).
cnf(c210,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c9,c45,c86,c88]) ).
cnf(c211,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c11,c19,c45,c210]) ).
cnf(c212,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c11,c211]) ).
cnf(c215,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c128,c212]) ).
cnf(c235,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c26,c215]) ).
cnf(c334,plain,
join(complement(one),complement(composition(converse(X),complement(X)))) = top,
inference(equational,[status(thm)],[c3,c117,c132,c140]) ).
cnf(c335,plain,
meet(one,composition(converse(X),complement(X))) = zero,
inference(equational,[status(thm)],[c26,c27,c334]) ).
cnf(c341,plain,
join(complement(one),complement(composition(X,complement(converse(X))))) = top,
inference(equational,[status(thm)],[c3,c117,c132,c148]) ).
cnf(c392,plain,
composition(join(one,one),composition(X,complement(Y))) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c13,c48,c215]) ).
cnf(c453,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(c454,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c453]) ).
cnf(c455,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c128,c454]) ).
cnf(c457,plain,
join(zero,meet(one,one)) = one,
inference(equational,[status(thm)],[c130,c140,c335,c454]) ).
cnf(c458,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c137,c455]) ).
cnf(c459,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c72,c131,c458]) ).
cnf(c460,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c455,c458]) ).
cnf(c461,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c458]) ).
cnf(c463,plain,
meet(one,one) = one,
inference(equational,[status(thm)],[c457,c458]) ).
cnf(c464,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c1,c235,c463]) ).
cnf(c466,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c31,c458,c460]) ).
cnf(c467,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c28,c466]) ).
cnf(c471,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c26,c455,c458]) ).
cnf(c472,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c31,c458,c466,c471]) ).
cnf(c484,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c454]) ).
cnf(c497,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c28,c484]) ).
cnf(c498,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c484]) ).
cnf(c502,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c497]) ).
cnf(c506,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c124,c471]) ).
cnf(c509,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c24,c471]) ).
cnf(c510,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c471,c509]) ).
cnf(c511,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c455,c458,c460,c510]) ).
cnf(c513,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c28,c511]) ).
cnf(c515,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c28,c513]) ).
cnf(c517,plain,
meet(X,meet(Y,complement(meet(X,Y)))) = zero,
inference(equational,[status(thm)],[c124,c459,c467,c471,c506,c515]) ).
cnf(c566,plain,
join(converse(X),complement(converse(meet(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c3,c116,c134,c498]) ).
cnf(c572,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c27,c39,c135,c454,c461]) ).
cnf(c575,plain,
complement(meet(converse(X),converse(complement(X)))) = top,
inference(equational,[status(thm)],[c2,c460,c471,c566,c572]) ).
cnf(c576,plain,
meet(converse(X),converse(complement(X))) = zero,
inference(equational,[status(thm)],[c467,c517,c575]) ).
cnf(c578,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c2,c576]) ).
cnf(c579,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c461,c502,c572,c578]) ).
cnf(c580,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c579]) ).
cnf(c581,plain,
complement(converse(X)) = converse(complement(X)),
inference(equational,[status(thm)],[c460,c580]) ).
cnf(c610,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(equational,[status(thm)],[c167,c458]) ).
cnf(c615,plain,
meet(complement(meet(X,Y)),join(complement(X),Y)) = complement(X),
inference(equational,[status(thm)],[c55,c454,c471]) ).
cnf(c620,plain,
meet(complement(meet(X,Y)),join(Y,complement(X))) = complement(X),
inference(equational,[status(thm)],[c3,c615]) ).
cnf(c654,plain,
meet(complement(meet(X,Y)),join(X,complement(Y))) = complement(Y),
inference(equational,[status(thm)],[c28,c620]) ).
cnf(c708,plain,
composition(converse(composition(X,join(converse(Y),Z))),W) = composition(join(Y,converse(Z)),composition(converse(X),W)),
inference(equational,[status(thm)],[c18,c52]) ).
cnf(c709,plain,
composition(converse(composition(X,top)),Y) = composition(top,composition(converse(X),Y)),
inference(equational,[status(thm)],[c2,c5,c581,c708]) ).
cnf(c752,plain,
converse(join(complement(X),composition(complement(composition(X,Y)),converse(Y)))) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c9,c88,c127,c581]) ).
cnf(c753,plain,
join(complement(X),composition(complement(composition(X,Y)),converse(Y))) = complement(X),
inference(equational,[status(thm)],[c2,c752]) ).
cnf(c754,plain,
join(X,composition(complement(composition(complement(X),Y)),converse(Y))) = X,
inference(equational,[status(thm)],[c31,c458,c460,c466,c753]) ).
cnf(c872,plain,
join(X,composition(complement(composition(complement(X),converse(Y))),Y)) = X,
inference(equational,[status(thm)],[c2,c754]) ).
cnf(c929,plain,
join(one,complement(composition(X,converse(complement(X))))) = complement(composition(X,converse(complement(X)))),
inference(equational,[status(thm)],[c341,c467,c472,c581,c654]) ).
cnf(c1382,plain,
join(one,complement(composition(complement(X),converse(X)))) = complement(composition(complement(X),converse(X))),
inference(equational,[status(thm)],[c31,c458,c460,c466,c929]) ).
cnf(c1434,plain,
composition(complement(composition(complement(X),converse(X))),X) = X,
inference(equational,[status(thm)],[c46,c872,c1382]) ).
cnf(c1436,plain,
composition(complement(composition(X,converse(complement(X)))),complement(X)) = complement(X),
inference(equational,[status(thm)],[c23,c392,c460,c464,c1434]) ).
cnf(c1437,plain,
converse(composition(complement(composition(X,top)),top)) = converse(complement(composition(X,top))),
inference(equational,[status(thm)],[c2,c145,c151,c459,c581,c610,c709,c1436]) ).
cnf(c1438,plain,
composition(complement(composition(X,top)),top) = complement(composition(X,top)),
inference(equational,[status(thm)],[c2,c1437]) ).
cnf(g1,plain,
complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top),
inference(equational,[status(thm)],[c1438]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL050-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.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 16:20:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 123.92/124.22 % SZS status Unsatisfiable
% 123.92/124.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------