%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL027-1 : 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 07:41:22 AM UTC 2025
% Result : Unsatisfiable 69.24s 69.49s
% Output : CNFRefutation 69.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 8 RR)
% Number of literals : 60 ( 59 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
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(sk1,one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c5,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c6,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c8,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c7]) ).
cnf(c9,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c10,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c12,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c14,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c16,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c20,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c12]) ).
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)],[c17,c21]) ).
cnf(c24,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c25,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c27,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c28,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c29,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c28]) ).
cnf(c30,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c6,c8,c29]) ).
cnf(c31,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c4,c29]) ).
cnf(c34,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c29,c30]) ).
cnf(c52,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c53,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c52]) ).
cnf(c98,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c12,c25]) ).
cnf(c107,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c24,c25]) ).
cnf(c162,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c163,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c162]) ).
cnf(c164,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c21,c23,c163]) ).
cnf(c165,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c30,c164]) ).
cnf(c174,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c14,c165]) ).
cnf(c232,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c14,c53]) ).
cnf(c233,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c21,c22,c27,c232]) ).
cnf(c234,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c3,c23,c233]) ).
cnf(c260,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c12,c53,c98,c107]) ).
cnf(c272,plain,
join(composition(X,converse(Y)),composition(X,Z)) = composition(X,join(converse(Y),Z)),
inference(equational,[status(thm)],[c2,c260]) ).
cnf(c273,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c272]) ).
cnf(c295,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c234,c273]) ).
cnf(c296,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c6,c295]) ).
cnf(c591,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(c592,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c29,c591]) ).
cnf(c593,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c8,c164,c592]) ).
cnf(c596,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c174,c593]) ).
cnf(c598,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c593,c596]) ).
cnf(c604,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c34,c596,c598]) ).
cnf(c609,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c29,c593,c596]) ).
cnf(c611,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c34,c596,c604,c609]) ).
cnf(c617,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c34,c596,c604,c611]) ).
cnf(c918,plain,
meet(X,complement(composition(sk1,top))) = meet(X,complement(composition(sk1,X))),
inference(equational,[status(thm)],[c296,c598,c617]) ).
cnf(c980,plain,
meet(one,complement(composition(sk1,top))) = meet(one,complement(sk1)),
inference(equational,[status(thm)],[c1,c918]) ).
cnf(g1,plain,
meet(complement(composition(sk1,top)),one) = meet(complement(sk1),one),
inference(equational,[status(thm)],[c31,c980]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL027-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.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 16:12:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 69.24/69.49 % SZS status Unsatisfiable
% 69.24/69.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------