%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL024-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 07:41:21 AM UTC 2025
% Result : Unsatisfiable 20.60s 20.75s
% Output : CNFRefutation 20.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 4 RR)
% Number of literals : 31 ( 30 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 : 57 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
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(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(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(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(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(c584,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(c585,plain,
join(complement(join(complement(X),Y)),complement(join(complement(X),complement(Y)))) = X,
inference(equational,[status(thm)],[c3,c584]) ).
cnf(c604,plain,
join(X,complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c3,c157,c585]) ).
cnf(c612,plain,
join(X,complement(join(Y,complement(X)))) = X,
inference(equational,[status(thm)],[c158,c604]) ).
cnf(c833,plain,
join(composition(converse(X),converse(Y)),composition(converse(X),converse(Z))) = composition(converse(X),join(converse(Y),converse(Z))),
inference(equational,[status(thm)],[c7,c8,c39]) ).
cnf(c834,plain,
join(composition(X,converse(Y)),composition(X,converse(Z))) = composition(X,join(converse(Y),converse(Z))),
inference(equational,[status(thm)],[c2,c833]) ).
cnf(c835,plain,
join(composition(X,Y),composition(X,converse(Z))) = composition(X,join(Y,converse(Z))),
inference(equational,[status(thm)],[c2,c834]) ).
cnf(c836,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c835]) ).
cnf(g1,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) = composition(meet(sk1,converse(sk2)),sk3),
inference(equational,[status(thm)],[c3,c18,c612,c836]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL024-1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 16:10:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 20.60/20.75 % SZS status Unsatisfiable
% 20.60/20.75 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------