%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL005-3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 07:41:15 AM UTC 2025
% Result : Unsatisfiable 94.47s 94.57s
% Output : CNFRefutation 94.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 9 RR)
% Number of literals : 117 ( 116 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 : 200 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
file('theBenchmark.p',goals_17) ).
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(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c20,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c20]) ).
cnf(c23,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c9]) ).
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(c38,plain,
converse(join(X,one)) = join(one,converse(X)),
inference(equational,[status(thm)],[c3,c17,c21]) ).
cnf(c40,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c41,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c42,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c43,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c42]) ).
cnf(c44,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c20,c21,c43]) ).
cnf(c45,plain,
join(X,composition(Y,X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c3,c20,c21,c43]) ).
cnf(c48,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c50,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c11,c15]) ).
cnf(c55,plain,
meet(join(complement(X),complement(Y)),Z) = complement(join(meet(X,Y),complement(Z))),
inference(equational,[status(thm)],[c26]) ).
cnf(c58,plain,
join(X,join(Y,complement(join(Y,X)))) = top,
inference(equational,[status(thm)],[c24,c48]) ).
cnf(c75,plain,
complement(join(meet(X,top),complement(Y))) = meet(join(zero,complement(X)),Y),
inference(equational,[status(thm)],[c3,c27,c55]) ).
cnf(c85,plain,
composition(X,join(one,converse(Y))) = join(X,composition(X,converse(Y))),
inference(equational,[status(thm)],[c18,c23,c38,c45]) ).
cnf(c86,plain,
composition(X,join(one,Y)) = join(X,composition(X,Y)),
inference(equational,[status(thm)],[c2,c85]) ).
cnf(c104,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c3,c5,c50]) ).
cnf(c110,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c114,plain,
join(X,composition(X,complement(one))) = composition(X,top),
inference(equational,[status(thm)],[c5,c86]) ).
cnf(c117,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c118,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c117]) ).
cnf(c119,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c20,c22,c118]) ).
cnf(c120,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c27,c119]) ).
cnf(c121,plain,
meet(X,X) = complement(complement(X)),
inference(equational,[status(thm)],[c26,c119]) ).
cnf(c122,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c41,c119]) ).
cnf(c123,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c34,c122]) ).
cnf(c124,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c3,c123]) ).
cnf(c125,plain,
converse(top) = top,
inference(equational,[status(thm)],[c110,c124]) ).
cnf(c126,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c114,c124]) ).
cnf(c128,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c120]) ).
cnf(c131,plain,
join(X,composition(top,X)) = composition(top,X),
inference(equational,[status(thm)],[c44,c123]) ).
cnf(c143,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c27,c118,c125,c126,c131]) ).
cnf(c191,plain,
join(composition(join(one,X),Y),Z) = join(Y,join(composition(X,Y),Z)),
inference(equational,[status(thm)],[c15,c44]) ).
cnf(c282,plain,
join(X,join(Y,composition(Z,X))) = join(composition(join(one,Z),X),Y),
inference(equational,[status(thm)],[c3,c191]) ).
cnf(c314,plain,
join(X,join(Y,composition(top,X))) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c123,c282]) ).
cnf(c429,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(c430,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c429]) ).
cnf(c431,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c119,c430]) ).
cnf(c433,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c128,c431]) ).
cnf(c435,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c431,c433]) ).
cnf(c436,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c143,c314,c433]) ).
cnf(c438,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c31,c433,c435]) ).
cnf(c439,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c28,c438]) ).
cnf(c442,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c26,c431,c433]) ).
cnf(c443,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c31,c433,c438,c442]) ).
cnf(c444,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c31,c433,c438,c442]) ).
cnf(c445,plain,
join(X,complement(meet(Y,X))) = top,
inference(equational,[status(thm)],[c41,c123,c442]) ).
cnf(c446,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c33,c122,c442]) ).
cnf(c448,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c431,c433,c443]) ).
cnf(c449,plain,
meet(X,join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c27,c430,c436,c444,c445]) ).
cnf(c450,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c435,c442,c443,c449]) ).
cnf(c451,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c31,c438,c449]) ).
cnf(c454,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c27,c430,c436,c443,c446]) ).
cnf(c455,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c31,c438,c454]) ).
cnf(c460,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c430]) ).
cnf(c471,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c460]) ).
cnf(c472,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c28,c460]) ).
cnf(c479,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c472]) ).
cnf(c485,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c24,c442]) ).
cnf(c486,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c442,c485]) ).
cnf(c487,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c31,c433,c435,c438,c486]) ).
cnf(c489,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c28,c487]) ).
cnf(c496,plain,
join(meet(complement(X),Y),complement(Z)) = complement(meet(join(X,complement(Y)),Z)),
inference(equational,[status(thm)],[c75,c433,c439,c442]) ).
cnf(c511,plain,
join(X,converse(meet(Y,converse(X)))) = X,
inference(equational,[status(thm)],[c2,c18,c450]) ).
cnf(c521,plain,
join(X,complement(meet(Y,join(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c58,c442]) ).
cnf(c523,plain,
meet(X,meet(Y,complement(meet(Y,X)))) = zero,
inference(equational,[status(thm)],[c26,c27,c442,c521]) ).
cnf(c524,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c436,c444,c451,c471,c489,c523]) ).
cnf(c527,plain,
join(X,meet(complement(X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c435,c455,c479,c524]) ).
cnf(c535,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c40,c125,c439,c524]) ).
cnf(c555,plain,
join(converse(X),complement(converse(meet(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c3,c104,c124,c471]) ).
cnf(c556,plain,
join(converse(X),complement(converse(meet(Y,X)))) = top,
inference(equational,[status(thm)],[c31,c438,c555]) ).
cnf(c576,plain,
meet(complement(converse(X)),converse(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c27,c448,c556]) ).
cnf(c579,plain,
meet(converse(X),converse(complement(X))) = zero,
inference(equational,[status(thm)],[c2,c28,c435,c535,c576]) ).
cnf(c580,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c2,c579]) ).
cnf(c581,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c436,c479,c535,c580]) ).
cnf(c582,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c581]) ).
cnf(c583,plain,
converse(complement(X)) = complement(converse(X)),
inference(equational,[status(thm)],[c2,c121,c535,c582]) ).
cnf(c590,plain,
join(X,converse(meet(converse(X),Y))) = X,
inference(equational,[status(thm)],[c28,c511]) ).
cnf(c633,plain,
complement(meet(join(X,Y),join(X,complement(Y)))) = complement(X),
inference(equational,[status(thm)],[c28,c430,c435,c496]) ).
cnf(c634,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c31,c433,c435,c438,c633]) ).
cnf(c636,plain,
meet(join(X,Y),join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c3,c634]) ).
cnf(c694,plain,
meet(join(X,Y),join(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c3,c636]) ).
cnf(c1276,plain,
join(X,converse(meet(complement(converse(X)),Y))) = join(X,converse(Y)),
inference(equational,[status(thm)],[c18,c527]) ).
cnf(c1277,plain,
converse(meet(converse(X),Y)) = meet(X,converse(Y)),
inference(equational,[status(thm)],[c435,c524,c583,c590,c694,c1276]) ).
cnf(c1279,plain,
meet(converse(X),converse(Y)) = converse(meet(X,Y)),
inference(equational,[status(thm)],[c2,c1277]) ).
cnf(g1,plain,
converse(meet(sk1,sk2)) = meet(converse(sk1),converse(sk2)),
inference(equational,[status(thm)],[c1279]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL005-3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Jul 14 16:07:34 EDT 2025
% 0.17/0.31 % CPUTime :
% 94.47/94.57 % SZS status Unsatisfiable
% 94.47/94.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------