%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL027-3 : 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 07:41:23 AM UTC 2025
% Result : Unsatisfiable 71.48s 71.51s
% Output : CNFRefutation 71.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 9 RR)
% Number of literals : 59 ( 58 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 : 89 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
file('theBenchmark.p',goals_18) ).
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_17) ).
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(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c10,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c12,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c14,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c16,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c21,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c22,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c23,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c24,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c23]) ).
cnf(c25,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c24]) ).
cnf(c26,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c17,c24]) ).
cnf(c27,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c16]) ).
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(c35,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c29,c30]) ).
cnf(c47,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c54,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c55,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c54]) ).
cnf(c56,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c24,c25,c55]) ).
cnf(c57,plain,
join(X,composition(Y,X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c4,c24,c25,c55]) ).
cnf(c58,plain,
join(X,composition(sk1,X)) = X,
inference(equational,[status(thm)],[c3,c26,c57]) ).
cnf(c122,plain,
composition(X,converse(join(one,Y))) = join(X,composition(X,converse(Y))),
inference(equational,[status(thm)],[c21,c22,c56]) ).
cnf(c125,plain,
join(X,composition(X,complement(one))) = composition(X,top),
inference(equational,[status(thm)],[c2,c25,c47,c122]) ).
cnf(c188,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c189,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c188]) ).
cnf(c190,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c24,c26,c189]) ).
cnf(c191,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c30,c190]) ).
cnf(c199,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c16,c191]) ).
cnf(c237,plain,
join(X,join(Y,composition(sk1,X))) = join(Y,X),
inference(equational,[status(thm)],[c27,c58]) ).
cnf(c266,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(equational,[status(thm)],[c125,c237]) ).
cnf(c673,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(c674,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c29,c673]) ).
cnf(c675,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c8,c190,c674]) ).
cnf(c677,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c199,c675]) ).
cnf(c680,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c675,c677]) ).
cnf(c684,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c35,c677,c680]) ).
cnf(c691,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c29,c675,c677]) ).
cnf(c692,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c35,c677,c684,c691]) ).
cnf(c693,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c35,c677,c684,c691]) ).
cnf(c696,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c35,c677,c684,c693]) ).
cnf(c697,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c35,c677,c684,c692]) ).
cnf(c1010,plain,
meet(one,complement(composition(sk1,top))) = meet(one,complement(sk1)),
inference(equational,[status(thm)],[c31,c266,c696,c697]) ).
cnf(g1,plain,
meet(complement(composition(sk1,top)),one) = meet(complement(sk1),one),
inference(equational,[status(thm)],[c31,c1010]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL027-3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 16:12:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 71.48/71.51 % SZS status Unsatisfiable
% 71.48/71.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------