%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:32:58 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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 : 113 ( 10 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
join(X0,top) = top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2] : join(X0_2,top) = top,
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
join(x0,top) != top,
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
join(X0_2,X1) = join(X1,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c5,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c8,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
join(X0_2,join(X1_2,X2)) = join(join(X0_2,X1_2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c11,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c13,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c17,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c11,c17]) ).
cnf(c19,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c9,c18]) ).
cnf(c20,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c23,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c25,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c31,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c24]) ).
cnf(c34,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c29,c34]) ).
cnf(c36,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c40,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c42,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c44,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c46,c35]) ).
cnf(c48,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c40,c47]) ).
cnf(c49,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = join(complement(X3),composition(converse(X),complement(composition(X,X3)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c54,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = join(composition(converse(X),complement(composition(X,X3))),complement(X3)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c56,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c52,c58]) ).
cnf(c60,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c38,c59]) ).
cnf(c61,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c63,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c21,c64]) ).
cnf(c66,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c6,c65]) ).
cnf(c67,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c70,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c71,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c66]) ).
cnf(c73,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c69,c73]) ).
cnf(c75,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
join(top,zero) = join(zero,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c78,plain,
join(zero,top) = join(top,zero),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c80,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,axiom,
meet(X0_2,X1_2) = complement(join(complement(X0_2),complement(X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c82,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c85,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c83,c86]) ).
cnf(c88,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c80,c87]) ).
cnf(c89,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c92,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
join(zero,top) = top,
inference(transitivity,[status(thm)],[c78,c93]) ).
cnf(c95,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c76,c94]) ).
cnf(c96,plain,
join(x0,top) = top,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
$false,
inference(resolution,[status(thm)],[c3,c96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:50:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 Command-line arguments: --no-flatten-goal
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48
% 0.17/0.48 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------