%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL018-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 07:41:19 AM UTC 2025
% Result : Unsatisfiable 1.09s 1.28s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 66 ( 66 unt; 0 nHn; 18 RR)
% Number of literals : 66 ( 65 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 : 76 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
composition(complement(sk1),top) != complement(sk1),
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,
composition(sk1,top) = sk1,
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,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c11,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c12,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c11]) ).
cnf(c15,plain,
composition(converse(one),converse(X)) = converse(X),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c16,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c17,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c18,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c21,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c22,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c23,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c6,c8,c22]) ).
cnf(c25,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c27,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c28,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c6,c27]) ).
cnf(c30,plain,
join(zero,join(top,X)) = join(top,X),
inference(equational,[status(thm)],[c21,c23,c27]) ).
cnf(c33,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c2,c25]) ).
cnf(c36,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c37,plain,
join(top,join(X,zero)) = join(X,top),
inference(equational,[status(thm)],[c23,c36]) ).
cnf(c38,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c40,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c4,c37]) ).
cnf(c41,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c68,plain,
join(zero,join(X,join(top,Y))) = join(top,join(X,Y)),
inference(equational,[status(thm)],[c21,c30]) ).
cnf(c82,plain,
join(X,join(Y,join(complement(X),Z))) = join(Y,join(top,Z)),
inference(equational,[status(thm)],[c21,c27]) ).
cnf(c83,plain,
join(top,join(X,join(zero,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c23,c82]) ).
cnf(c87,plain,
join(X,top) = join(top,join(X,join(zero,zero))),
inference(equational,[status(thm)],[c6,c23,c83]) ).
cnf(c88,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c89,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c88]) ).
cnf(c90,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c16,c18,c89]) ).
cnf(c91,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c23,c90]) ).
cnf(c92,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c4,c6,c30,c41,c68,c87,c90,c91]) ).
cnf(c93,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c28,c92]) ).
cnf(c94,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c40,c87,c91,c93]) ).
cnf(c95,plain,
converse(top) = top,
inference(equational,[status(thm)],[c33,c94]) ).
cnf(c97,plain,
join(zero,composition(converse(sk1),complement(sk1))) = zero,
inference(equational,[status(thm)],[c3,c23,c89]) ).
cnf(c100,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c12,c91]) ).
cnf(c127,plain,
join(X,join(Y,join(Z,complement(X)))) = top,
inference(equational,[status(thm)],[c21,c36,c93]) ).
cnf(c147,plain,
join(composition(top,X),composition(Y,X)) = composition(top,X),
inference(equational,[status(thm)],[c38,c94]) ).
cnf(c148,plain,
join(X,composition(top,X)) = composition(top,X),
inference(equational,[status(thm)],[c4,c16,c147]) ).
cnf(c261,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(c262,plain,
join(complement(join(complement(X),Y)),complement(join(complement(X),complement(Y)))) = X,
inference(equational,[status(thm)],[c4,c261]) ).
cnf(c263,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c4,c6,c23,c90,c262]) ).
cnf(c264,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c100,c263]) ).
cnf(c265,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c6,c264]) ).
cnf(c266,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c263,c264]) ).
cnf(c267,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c4,c264]) ).
cnf(c269,plain,
join(complement(X),join(Y,X)) = top,
inference(equational,[status(thm)],[c127,c263]) ).
cnf(c271,plain,
converse(complement(converse(zero))) = top,
inference(equational,[status(thm)],[c33,c95,c264]) ).
cnf(c272,plain,
complement(converse(zero)) = top,
inference(equational,[status(thm)],[c2,c95,c271]) ).
cnf(c273,plain,
converse(zero) = zero,
inference(equational,[status(thm)],[c23,c266,c272]) ).
cnf(c275,plain,
complement(composition(converse(sk1),complement(sk1))) = top,
inference(equational,[status(thm)],[c97,c267,c269]) ).
cnf(c276,plain,
composition(converse(sk1),complement(sk1)) = zero,
inference(equational,[status(thm)],[c23,c91,c263,c275]) ).
cnf(c277,plain,
composition(converse(complement(sk1)),sk1) = zero,
inference(equational,[status(thm)],[c2,c10,c273,c276]) ).
cnf(c340,plain,
join(converse(complement(X)),composition(converse(complement(composition(Y,X))),Y)) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c9,c10,c89]) ).
cnf(c341,plain,
composition(top,converse(complement(sk1))) = converse(complement(sk1)),
inference(equational,[status(thm)],[c95,c148,c265,c277,c340]) ).
cnf(c342,plain,
composition(complement(sk1),top) = complement(sk1),
inference(equational,[status(thm)],[c2,c10,c95,c341]) ).
cnf(g1,plain,
composition(complement(sk1),top) = complement(sk1),
inference(equational,[status(thm)],[c342]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL018-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 16:09:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.09/1.28 % SZS status Unsatisfiable
% 1.09/1.28 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------