%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:33:02 PM UTC 2026
% Result : Theorem 2.98s 0.89s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] : composition(X0_2,join(X1_2,X2_2)) = join(composition(X0_2,X1_2),composition(X0_2,X2_2)),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
composition(x0,join(x1,x2)) != join(composition(x0,x1),composition(x0,x2)),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c5,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
join(composition(X3,X4),composition(X3,X)) = join(composition(X3,X4),composition(X3,converse(converse(X)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c10,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
composition(X3,converse(X)) = composition(converse(converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
join(composition(X4,X3),composition(X4,converse(X))) = join(composition(X4,X3),composition(converse(converse(X4)),converse(X))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c14,plain,
converse(composition(X,converse(X3))) = composition(converse(converse(X3)),converse(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
composition(converse(converse(X3)),converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = join(composition(X4,X3),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
converse(converse(composition(X3,X))) = composition(X3,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c18,plain,
composition(X3,X) = converse(converse(composition(X3,X))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c21,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c24,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c26,plain,
composition(join(converse(X3),X4),converse(X)) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(converse(X3),X4),converse(X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c29,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
composition(join(converse(X3),X4),converse(X)) = composition(join(X4,converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c27,c30]) ).
cnf(c32,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c24,c31]) ).
cnf(c33,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = composition(join(X,converse(X3)),converse(X4)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = converse(composition(join(X,converse(X3)),converse(X4))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(converse(converse(X4)),converse(join(X,converse(X3)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c36,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c37,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,converse(join(X,converse(X3)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
converse(join(X,converse(X3))) = join(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c39,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(converse(X),converse(converse(X3)))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c41,plain,
join(converse(X),converse(converse(X3))) = join(converse(X),X3),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(converse(X),X3)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c44,plain,
composition(X4,join(converse(X),X3)) = composition(X4,join(X3,converse(X))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c39,c45]) ).
cnf(c47,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c37,c46]) ).
cnf(c48,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c35,c47]) ).
cnf(c49,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c34,c48]) ).
cnf(c50,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c22,c49]) ).
cnf(c51,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c19,c50]) ).
cnf(c52,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c16,c51]) ).
cnf(c53,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c12,c52]) ).
cnf(c54,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,converse(converse(X)))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c56,plain,
join(X3,converse(converse(X))) = join(X3,X),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
composition(X4,join(X3,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
join(composition(X4,X3),composition(X4,X)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c8,c58]) ).
cnf(c60,plain,
join(composition(x0,x1),composition(x0,x2)) = composition(x0,join(x1,x2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
composition(x0,join(x1,x2)) = join(composition(x0,x1),composition(x0,x2)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
$false,
inference(resolution,[status(thm)],[c3,c61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:55:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.98/0.89 Command-line arguments: --flatten --complete-subsets
% 2.98/0.89
% 2.98/0.89 % SZS status Theorem
% 2.98/0.89
% 2.98/0.89 % SZS output start CNFRefutation
% See solution above
% 3.81/0.91
% 3.81/0.91 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------