%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL042-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 07:41:28 AM UTC 2025
% Result : Unsatisfiable 91.98s 92.16s
% Output : CNFRefutation 91.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 101 ( 101 unt; 0 nHn; 18 RR)
% Number of literals : 101 ( 100 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 : 163 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(composition(converse(sk1),sk1),one) != 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(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,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c7,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c9,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c11,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c13,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c15,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c17,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c18,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c19,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c20,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c20]) ).
cnf(c23,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c24,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c25,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c26,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c25]) ).
cnf(c27,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c5,c7,c26]) ).
cnf(c28,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c31,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c26,c27]) ).
cnf(c32,plain,
complement(join(zero,zero)) = meet(top,top),
inference(equational,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c34,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c5,c33]) ).
cnf(c37,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c40,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c41,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c42,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c41]) ).
cnf(c43,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c20,c21,c42]) ).
cnf(c46,axiom,
meet(composition(sk1,X),composition(sk1,complement(X))) = zero,
file('theBenchmark.p',goals_14) ).
cnf(c47,plain,
meet(sk1,composition(sk1,complement(one))) = zero,
inference(equational,[status(thm)],[c1,c46]) ).
cnf(c56,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c26]) ).
cnf(c57,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c26]) ).
cnf(c66,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c5,c15,c26]) ).
cnf(c67,plain,
join(zero,join(complement(X),meet(top,X))) = top,
inference(equational,[status(thm)],[c27,c66]) ).
cnf(c68,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c27,c67]) ).
cnf(c78,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c17,c23]) ).
cnf(c82,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c18,c23]) ).
cnf(c86,plain,
join(converse(X),composition(converse(Y),Z)) = converse(join(X,composition(converse(Z),Y))),
inference(equational,[status(thm)],[c17,c19]) ).
cnf(c87,plain,
converse(join(X,composition(X,Y))) = converse(composition(X,join(one,Y))),
inference(equational,[status(thm)],[c2,c9,c37,c43,c86]) ).
cnf(c88,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c87]) ).
cnf(c107,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c120,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c121,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c120]) ).
cnf(c122,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c20,c22,c121]) ).
cnf(c123,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c27,c122]) ).
cnf(c125,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c32,c123]) ).
cnf(c126,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c40,c122]) ).
cnf(c127,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c34,c126]) ).
cnf(c129,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c3,c127]) ).
cnf(c130,plain,
converse(top) = top,
inference(equational,[status(thm)],[c107,c129]) ).
cnf(c134,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c123]) ).
cnf(c139,plain,
composition(top,join(one,X)) = top,
inference(equational,[status(thm)],[c88,c129]) ).
cnf(c140,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c5,c139]) ).
cnf(c141,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c27,c43,c121,c127,c130,c140]) ).
cnf(c163,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(equational,[status(thm)],[c27,c121]) ).
cnf(c188,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c204,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c9,c42,c78,c82]) ).
cnf(c216,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c204]) ).
cnf(c217,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c216]) ).
cnf(c292,plain,
join(composition(X,Y),join(Z,composition(W,Y))) = join(composition(join(W,X),Y),Z),
inference(equational,[status(thm)],[c3,c15,c188]) ).
cnf(c296,plain,
join(composition(X,Y),join(Z,Y)) = join(composition(join(one,X),Y),Z),
inference(equational,[status(thm)],[c20,c21,c292]) ).
cnf(c300,plain,
join(composition(X,Y),join(Z,Y)) = join(Z,composition(join(one,X),Y)),
inference(equational,[status(thm)],[c3,c296]) ).
cnf(c308,plain,
join(X,join(composition(Y,X),Z)) = join(Z,composition(join(one,Y),X)),
inference(equational,[status(thm)],[c3,c24,c300]) ).
cnf(c342,plain,
join(X,join(composition(top,X),Y)) = join(Y,composition(top,X)),
inference(equational,[status(thm)],[c127,c308]) ).
cnf(c460,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(c461,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c460]) ).
cnf(c462,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c122,c461]) ).
cnf(c465,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c134,c462]) ).
cnf(c466,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c68,c125,c465]) ).
cnf(c467,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c141,c342,c465]) ).
cnf(c468,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c462,c465]) ).
cnf(c472,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c5,c27,c461,c467,c468]) ).
cnf(c473,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c57,c122,c472]) ).
cnf(c474,plain,
meet(zero,complement(X)) = zero,
inference(equational,[status(thm)],[c27,c32,c123,c125,c129,c466,c473]) ).
cnf(c476,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c56,c129,c465,c466,c468,c474]) ).
cnf(c479,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c56,c122,c472]) ).
cnf(c480,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c31,c465,c476,c479]) ).
cnf(c481,plain,
meet(complement(X),complement(Y)) = complement(join(X,Y)),
inference(equational,[status(thm)],[c31,c465,c476,c479]) ).
cnf(c495,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c461]) ).
cnf(c497,plain,
meet(sk1,complement(composition(sk1,complement(one)))) = sk1,
inference(equational,[status(thm)],[c47,c465,c495]) ).
cnf(c507,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c495]) ).
cnf(c513,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c507]) ).
cnf(c517,plain,
join(sk1,complement(composition(sk1,top))) = complement(composition(sk1,complement(one))),
inference(equational,[status(thm)],[c5,c88,c481,c497,c513]) ).
cnf(c710,plain,
meet(X,complement(composition(converse(Y),complement(composition(Y,X))))) = X,
inference(equational,[status(thm)],[c121,c468,c473]) ).
cnf(c957,plain,
join(X,composition(converse(Y),complement(composition(Y,complement(X))))) = X,
inference(equational,[status(thm)],[c468,c480,c710]) ).
cnf(c1093,plain,
join(composition(X,Y),join(Z,composition(X,W))) = join(Z,composition(X,join(Y,W))),
inference(equational,[status(thm)],[c24,c217]) ).
cnf(c1289,plain,
composition(converse(X),join(Y,complement(composition(X,top)))) = composition(converse(X),Y),
inference(equational,[status(thm)],[c163,c465,c467,c1093]) ).
cnf(c1405,plain,
composition(converse(sk1),complement(composition(sk1,complement(one)))) = composition(converse(sk1),sk1),
inference(equational,[status(thm)],[c517,c1289]) ).
cnf(c1406,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(equational,[status(thm)],[c957,c1405]) ).
cnf(g1,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(equational,[status(thm)],[c3,c1406]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL042-1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n009.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 16:18:34 EDT 2025
% 0.20/0.34 % CPUTime :
% 91.98/92.16 % SZS status Unsatisfiable
% 91.98/92.16 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------