%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL004-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 10.69s 10.82s
% Output : CNFRefutation 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 12 RR)
% Number of literals : 97 ( 96 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 146 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
converse(complement(sk1)) != complement(converse(sk1)),
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,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c6,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c8,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
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(c13,plain,
composition(converse(one),converse(X)) = converse(X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c14,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c15,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c16,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c18,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c19,plain,
converse(top) = join(converse(X),converse(complement(X))),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c20,plain,
join(top,X) = join(Y,join(complement(Y),X)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c21,plain,
join(X,top) = join(top,complement(complement(X))),
inference(equational,[status(thm)],[c4,c20]) ).
cnf(c23,plain,
join(top,complement(complement(X))) = join(top,X),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c24,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c26,plain,
join(X,join(Y,complement(X))) = join(top,Y),
inference(equational,[status(thm)],[c3,c20]) ).
cnf(c28,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(equational,[status(thm)],[c6,c18]) ).
cnf(c29,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c33,plain,
complement(join(X,complement(X))) = zero,
inference(equational,[status(thm)],[c4,c29]) ).
cnf(c37,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c26,c29]) ).
cnf(c38,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c39,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c38]) ).
cnf(c40,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c14,c15,c39]) ).
cnf(c52,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c53,plain,
join(converse(X),converse(complement(X))) = join(converse(Y),converse(complement(Y))),
inference(equational,[status(thm)],[c4,c8,c19]) ).
cnf(c60,plain,
join(X,composition(complement(one),X)) = composition(top,X),
inference(equational,[status(thm)],[c4,c40]) ).
cnf(c63,plain,
top = join(X,join(Y,complement(join(Y,X)))),
inference(equational,[status(thm)],[c17,c52]) ).
cnf(c64,plain,
join(X,converse(complement(converse(X)))) = join(converse(Y),converse(complement(Y))),
inference(equational,[status(thm)],[c2,c53]) ).
cnf(c79,plain,
join(X,join(Y,complement(join(X,Y)))) = join(Z,complement(Z)),
inference(equational,[status(thm)],[c4,c52]) ).
cnf(c106,plain,
join(X,converse(top)) = join(converse(Y),join(X,converse(complement(Y)))),
inference(equational,[status(thm)],[c17,c19]) ).
cnf(c111,plain,
join(X,join(Y,join(complement(Y),Z))) = join(top,join(X,Z)),
inference(equational,[status(thm)],[c17,c20]) ).
cnf(c115,plain,
join(X,join(top,Y)) = join(Z,join(X,join(complement(Z),Y))),
inference(equational,[status(thm)],[c17,c20]) ).
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)],[c14,c16,c124]) ).
cnf(c126,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c33,c125]) ).
cnf(c127,plain,
join(X,complement(X)) = join(top,complement(X)),
inference(equational,[status(thm)],[c26,c125]) ).
cnf(c128,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c33,c37,c52,c127]) ).
cnf(c129,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c23,c128]) ).
cnf(c130,plain,
converse(top) = top,
inference(equational,[status(thm)],[c24,c129]) ).
cnf(c131,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c21,c128]) ).
cnf(c132,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c60,c129]) ).
cnf(c134,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(equational,[status(thm)],[c17,c126]) ).
cnf(c135,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c12,c126]) ).
cnf(c141,plain,
join(zero,composition(top,zero)) = composition(top,zero),
inference(equational,[status(thm)],[c60,c135]) ).
cnf(c145,plain,
join(X,join(Y,complement(Y))) = top,
inference(equational,[status(thm)],[c111,c125,c129]) ).
cnf(c151,plain,
complement(join(X,join(Y,complement(Y)))) = zero,
inference(equational,[status(thm)],[c29,c145]) ).
cnf(c157,plain,
join(complement(X),join(complement(X),Y)) = join(complement(X),Y),
inference(equational,[status(thm)],[c12,c125]) ).
cnf(c158,plain,
join(complement(X),join(Y,complement(X))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c17,c125]) ).
cnf(c159,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c29,c124,c130,c132,c141]) ).
cnf(c167,plain,
top = join(X,join(Y,join(zero,complement(X)))),
inference(equational,[status(thm)],[c3,c4,c29,c115,c131]) ).
cnf(c183,plain,
join(converse(X),join(Y,converse(complement(X)))) = top,
inference(equational,[status(thm)],[c3,c106,c129,c130]) ).
cnf(c193,plain,
join(X,join(converse(Y),complement(X))) = join(converse(Z),converse(complement(Z))),
inference(equational,[status(thm)],[c2,c8,c24,c64,c183]) ).
cnf(c194,plain,
join(X,join(Y,complement(X))) = join(converse(Z),converse(complement(Z))),
inference(equational,[status(thm)],[c2,c193]) ).
cnf(c198,plain,
complement(join(converse(X),converse(complement(X)))) = zero,
inference(equational,[status(thm)],[c151,c194]) ).
cnf(c199,plain,
complement(join(X,join(Y,complement(join(Y,X))))) = zero,
inference(equational,[status(thm)],[c29,c63]) ).
cnf(c200,plain,
complement(join(X,join(Y,complement(join(X,Y))))) = zero,
inference(equational,[status(thm)],[c28,c79]) ).
cnf(c205,plain,
join(composition(join(X,Y),Z),W) = join(composition(X,Z),join(composition(Y,Z),W)),
inference(equational,[status(thm)],[c12,c39]) ).
cnf(c312,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(W,composition(join(X,Z),Y)),
inference(equational,[status(thm)],[c3,c205]) ).
cnf(c323,plain,
complement(join(X,join(Y,join(zero,complement(X))))) = zero,
inference(equational,[status(thm)],[c3,c12,c29,c134,c167,c200]) ).
cnf(c365,plain,
top = join(complement(composition(X,Y)),composition(join(Z,X),Y)),
inference(equational,[status(thm)],[c4,c131,c312]) ).
cnf(c383,plain,
join(complement(composition(complement(X),Y)),composition(top,Y)) = top,
inference(equational,[status(thm)],[c4,c365]) ).
cnf(c384,plain,
join(complement(composition(zero,X)),composition(top,X)) = top,
inference(equational,[status(thm)],[c33,c383]) ).
cnf(c395,plain,
complement(join(X,join(zero,converse(complement(converse(X)))))) = zero,
inference(equational,[status(thm)],[c3,c17,c64,c198,c199]) ).
cnf(c441,plain,
top = join(zero,complement(composition(zero,zero))),
inference(equational,[status(thm)],[c3,c159,c384]) ).
cnf(c442,plain,
join(zero,join(X,complement(join(zero,X)))) = join(zero,complement(composition(zero,zero))),
inference(equational,[status(thm)],[c12,c52,c135,c441]) ).
cnf(c444,plain,
complement(join(zero,complement(composition(zero,zero)))) = zero,
inference(equational,[status(thm)],[c126,c135,c323,c442]) ).
cnf(c501,plain,
join(zero,complement(composition(zero,zero))) = join(X,complement(X)),
inference(equational,[status(thm)],[c4,c441]) ).
cnf(c573,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(c574,plain,
join(complement(join(complement(X),Y)),complement(join(complement(X),complement(Y)))) = X,
inference(equational,[status(thm)],[c3,c573]) ).
cnf(c575,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c3,c125,c444,c501,c574]) ).
cnf(c576,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c135,c575]) ).
cnf(c577,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c575,c576]) ).
cnf(c578,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c576]) ).
cnf(c592,plain,
join(X,complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c3,c157,c574]) ).
cnf(c601,plain,
join(complement(X),complement(join(X,Y))) = complement(X),
inference(equational,[status(thm)],[c125,c157,c577,c592]) ).
cnf(c673,plain,
join(complement(join(X,complement(Y))),complement(join(complement(Y),complement(X)))) = Y,
inference(equational,[status(thm)],[c3,c574]) ).
cnf(c674,plain,
join(complement(X),complement(join(complement(X),complement(Y)))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c3,c12,c601,c673]) ).
cnf(c675,plain,
join(complement(X),complement(join(Y,complement(X)))) = join(complement(X),complement(Y)),
inference(equational,[status(thm)],[c12,c158,c577,c601,c673,c674]) ).
cnf(c676,plain,
join(complement(X),complement(join(complement(X),Y))) = join(complement(X),complement(Y)),
inference(equational,[status(thm)],[c3,c675]) ).
cnf(c678,plain,
join(X,complement(join(Y,X))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c577,c675]) ).
cnf(c683,plain,
join(complement(X),complement(converse(complement(converse(complement(X)))))) = complement(X),
inference(equational,[status(thm)],[c395,c576,c578,c676]) ).
cnf(c684,plain,
join(X,converse(complement(converse(complement(X))))) = converse(complement(converse(complement(X)))),
inference(equational,[status(thm)],[c577,c673,c678,c683]) ).
cnf(c685,plain,
join(X,complement(converse(complement(converse(X))))) = X,
inference(equational,[status(thm)],[c3,c574,c577,c675,c684]) ).
cnf(c686,plain,
converse(complement(converse(complement(converse(X))))) = converse(X),
inference(equational,[status(thm)],[c8,c684,c685]) ).
cnf(c687,plain,
complement(converse(complement(converse(X)))) = X,
inference(equational,[status(thm)],[c2,c686]) ).
cnf(c688,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c687]) ).
cnf(c689,plain,
converse(complement(X)) = complement(converse(X)),
inference(equational,[status(thm)],[c577,c688]) ).
cnf(g1,plain,
converse(complement(sk1)) = complement(converse(sk1)),
inference(equational,[status(thm)],[c689]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL004-1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 16:07:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 10.69/10.82 % SZS status Unsatisfiable
% 10.69/10.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------