%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:33:21 PM UTC 2026
% Result : Theorem 1.39s 0.60s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 160 ( 151 unt; 0 def)
% Number of atoms : 178 ( 177 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 7 ~; 0 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 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 : 255 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1] :
( ( join(composition(converse(X0),X0),one) = one
& join(composition(converse(X1),X1),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2] :
( ( join(composition(converse(X0_2),X0_2),one) = one
& join(composition(converse(X1_2),X1_2),one) = one )
=> join(composition(converse(composition(X0_2,X1_2)),composition(X0_2,X1_2)),one) = one ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( join(composition(converse(x0),x0),one) = one
& join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) != one
& join(composition(converse(x1),x1),one) = one ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) != one,
inference(clausify,[status(thm)],[c3]) ).
fof(c5,conjecture,
! [X0_2,X1_2] :
( ( join(composition(converse(X0_2),X0_2),one) = one
& join(composition(converse(X1_2),X1_2),one) = one )
=> join(composition(converse(composition(X0_2,X1_2)),composition(X0_2,X1_2)),one) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c6,negated_conjecture,
~ ! [X0_2,X1_2] :
( ( join(composition(converse(X0_2),X0_2),one) = one
& join(composition(converse(X1_2),X1_2),one) = one )
=> join(composition(converse(composition(X0_2,X1_2)),composition(X0_2,X1_2)),one) = one ),
inference(negate_conjecture,[status(cth)],[c5]) ).
fof(c7,plain,
( join(composition(converse(x0),x0),one) = one
& join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) != one
& join(composition(converse(x1),x1),one) = one ),
inference(clausify,[status(esa)],[c6]) ).
cnf(c8,plain,
join(composition(converse(x1),x1),one) = one,
inference(clausify,[status(thm)],[c7]) ).
cnf(c9,plain,
join(join(composition(converse(x1),x1),one),X) = join(one,X),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c11,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
join(join(composition(converse(x1),x1),one),X) = join(X,one),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
join(join(composition(converse(x1),x1),one),composition(converse(composition(x0,x1)),composition(x0,x1))) = join(composition(converse(composition(x0,x1)),composition(x0,x1)),one),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) = join(join(composition(converse(x1),x1),one),composition(converse(composition(x0,x1)),composition(x0,x1))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),join(composition(converse(x1),x1),one)) = join(join(composition(converse(x1),x1),one),composition(converse(composition(x0,x1)),composition(x0,x1))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c17,plain,
join(join(composition(converse(x1),x1),one),composition(converse(composition(x0,x1)),composition(x0,x1))) = join(composition(converse(composition(x0,x1)),composition(x0,x1)),join(composition(converse(x1),x1),one)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c19,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
join(join(composition(converse(x1),x1),one),join(X3,X)) = join(join(composition(converse(x1),x1),one),join(X,X3)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
join(X0_2,join(X1_2,X2)) = join(join(X0_2,X1_2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c22,plain,
join(join(composition(converse(x1),x1),one),join(X,X3)) = join(join(join(composition(converse(x1),x1),one),X),X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
join(join(join(composition(converse(x1),x1),one),X),X3) = join(join(X,one),X3),
inference(congruence,[status(thm)],[c13]) ).
cnf(c24,plain,
join(join(X,one),X3) = join(X3,join(X,one)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c25,plain,
join(join(join(composition(converse(x1),x1),one),X),X3) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
join(join(composition(converse(x1),x1),one),join(X,X3)) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
join(join(composition(converse(x1),x1),one),join(X3,X)) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c20,c26]) ).
cnf(c28,plain,
join(join(composition(converse(x1),x1),one),join(composition(converse(composition(x0,x1)),composition(x0,x1)),composition(converse(x1),x1))) = join(composition(converse(composition(x0,x1)),composition(x0,x1)),join(composition(converse(x1),x1),one)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),join(composition(converse(x1),x1),one)) = join(join(composition(converse(x1),x1),one),join(composition(converse(composition(x0,x1)),composition(x0,x1)),composition(converse(x1),x1))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
join(composition(converse(X3),X),composition(converse(composition(x0,X3)),composition(x0,X))) = join(composition(converse(composition(x0,X3)),composition(x0,X)),composition(converse(X3),X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c31,plain,
join(composition(converse(composition(x0,X3)),composition(x0,X)),composition(converse(X3),X)) = join(composition(converse(X3),X),composition(converse(composition(x0,X3)),composition(x0,X))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c33,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
composition(converse(composition(X,X3)),X4) = composition(composition(converse(X3),converse(X)),X4),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c36,plain,
composition(converse(X4),composition(converse(X3),X)) = composition(composition(converse(X4),converse(X3)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
composition(composition(converse(X4),converse(X3)),X) = composition(converse(X4),composition(converse(X3),X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
composition(converse(composition(X3,X4)),X) = composition(converse(X4),composition(converse(X3),X)),
inference(transitivity,[status(thm)],[c34,c37]) ).
cnf(c39,plain,
composition(converse(composition(X3,X4)),composition(X,X5)) = composition(converse(X4),composition(converse(X3),composition(X,X5))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
composition(converse(X4),composition(X3,X)) = composition(composition(converse(X4),X3),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c41,plain,
composition(converse(X5),composition(converse(X4),composition(X3,X))) = composition(converse(X5),composition(composition(converse(X4),X3),X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
composition(converse(composition(X4,X5)),composition(X3,X)) = composition(converse(X5),composition(composition(converse(X4),X3),X)),
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
composition(converse(composition(x0,X3)),composition(x0,X)) = composition(converse(X3),composition(composition(converse(x0),x0),X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
join(composition(converse(X3),X),composition(converse(composition(x0,X3)),composition(x0,X))) = join(composition(converse(X3),X),composition(converse(X3),composition(composition(converse(x0),x0),X))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c46,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
composition(converse(X3),X) = composition(converse(X3),converse(converse(X))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
join(composition(converse(X4),X3),composition(converse(X4),X)) = join(composition(converse(X4),X3),composition(converse(X4),converse(converse(X)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c51,plain,
composition(converse(X3),converse(X)) = converse(composition(X,X3)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
join(composition(converse(X4),X3),composition(converse(X4),converse(X))) = join(composition(converse(X4),X3),converse(composition(X,X4))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c54,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c55,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
converse(composition(converse(X),X3)) = composition(converse(X3),X),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
composition(converse(X3),X) = converse(composition(converse(X),X3)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
join(composition(converse(X4),X3),converse(composition(X,X4))) = join(converse(composition(converse(X3),X4)),converse(composition(X,X4))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c61,plain,
converse(join(composition(converse(X3),X4),composition(X,X4))) = join(converse(composition(converse(X3),X4)),converse(composition(X,X4))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
join(converse(composition(converse(X3),X4)),converse(composition(X,X4))) = converse(join(composition(converse(X3),X4),composition(X,X4))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c64,plain,
composition(join(X3,X4),X) = join(composition(X3,X),composition(X4,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
join(composition(X3,X),composition(X4,X)) = composition(join(X3,X4),X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c67,plain,
composition(join(X3,X4),X) = composition(join(X4,X3),X),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
join(composition(X3,X),composition(X4,X)) = composition(join(X4,X3),X),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
join(composition(converse(X3),X4),composition(X,X4)) = composition(join(X,converse(X3)),X4),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
converse(join(composition(converse(X3),X4),composition(X,X4))) = converse(composition(join(X,converse(X3)),X4)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
converse(composition(join(X,converse(X3)),X4)) = composition(converse(X4),converse(join(X,converse(X3)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c72,plain,
converse(join(X,converse(X3))) = join(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c73,plain,
composition(converse(X4),converse(join(X,converse(X3)))) = composition(converse(X4),join(converse(X),converse(converse(X3)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c75,plain,
join(converse(X),converse(converse(X3))) = join(converse(X),X3),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
composition(converse(X4),join(converse(X),converse(converse(X3)))) = composition(converse(X4),join(converse(X),X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c78,plain,
composition(converse(X4),join(converse(X),X3)) = composition(converse(X4),join(X3,converse(X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
composition(converse(X4),join(converse(X),converse(converse(X3)))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
composition(converse(X4),converse(join(X,converse(X3)))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c73,c79]) ).
cnf(c81,plain,
converse(composition(join(X,converse(X3)),X4)) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c71,c80]) ).
cnf(c82,plain,
converse(join(composition(converse(X3),X4),composition(X,X4))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c70,c81]) ).
cnf(c83,plain,
join(converse(composition(converse(X3),X4)),converse(composition(X,X4))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c62,c82]) ).
cnf(c84,plain,
join(composition(converse(X4),X3),converse(composition(X,X4))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c59,c83]) ).
cnf(c85,plain,
join(composition(converse(X4),X3),composition(converse(X4),converse(X))) = composition(converse(X4),join(X3,converse(X))),
inference(transitivity,[status(thm)],[c52,c84]) ).
cnf(c86,plain,
join(composition(converse(X4),X3),composition(converse(X4),converse(converse(X)))) = composition(converse(X4),join(X3,converse(converse(X)))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c88,plain,
join(X3,converse(converse(X))) = join(X3,X),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
composition(converse(X4),join(X3,converse(converse(X)))) = composition(converse(X4),join(X3,X)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
join(composition(converse(X4),X3),composition(converse(X4),converse(converse(X)))) = composition(converse(X4),join(X3,X)),
inference(transitivity,[status(thm)],[c86,c89]) ).
cnf(c91,plain,
join(composition(converse(X4),X3),composition(converse(X4),X)) = composition(converse(X4),join(X3,X)),
inference(transitivity,[status(thm)],[c49,c90]) ).
cnf(c92,plain,
join(composition(converse(X3),X),composition(converse(X3),composition(composition(converse(x0),x0),X))) = composition(converse(X3),join(X,composition(composition(converse(x0),x0),X))),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
join(X,join(composition(converse(x1),x1),one)) = join(join(composition(converse(x1),x1),one),X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c94,plain,
join(join(composition(converse(x1),x1),one),X) = join(X,join(composition(converse(x1),x1),one)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
composition(join(join(composition(converse(x1),x1),one),X),X3) = composition(join(X,join(composition(converse(x1),x1),one)),X3),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
join(join(composition(converse(x1),x1),one),X) = join(X,join(composition(converse(x1),x1),one)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c97,plain,
join(X,join(composition(converse(x1),x1),one)) = join(join(composition(converse(x1),x1),one),X),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
composition(join(X3,join(composition(converse(x1),x1),one)),X) = composition(join(join(composition(converse(x1),x1),one),X3),X),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
cnf(c100,plain,
composition(converse(join(composition(converse(x1),x1),one)),one) = converse(join(composition(converse(x1),x1),one)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
converse(join(composition(converse(x1),x1),one)) = composition(converse(join(composition(converse(x1),x1),one)),one),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c103,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
composition(converse(join(composition(converse(x1),x1),one)),X) = composition(converse(join(composition(converse(x1),x1),one)),converse(converse(X))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
converse(join(composition(converse(x1),x1),one)) = converse(one),
inference(congruence,[status(thm)],[c8]) ).
cnf(c106,plain,
composition(converse(join(composition(converse(x1),x1),one)),converse(X)) = composition(converse(one),converse(X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c108,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c110,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
composition(converse(join(composition(converse(x1),x1),one)),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c106,c111]) ).
cnf(c113,plain,
composition(converse(join(composition(converse(x1),x1),one)),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c115,plain,
composition(converse(join(composition(converse(x1),x1),one)),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
composition(converse(join(composition(converse(x1),x1),one)),X) = X,
inference(transitivity,[status(thm)],[c104,c115]) ).
cnf(c117,plain,
composition(converse(join(composition(converse(x1),x1),one)),one) = one,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
one = join(composition(converse(x1),x1),one),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c119,plain,
composition(converse(join(composition(converse(x1),x1),one)),one) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
converse(join(composition(converse(x1),x1),one)) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c101,c119]) ).
cnf(c121,plain,
join(composition(converse(x1),x1),one) = converse(join(composition(converse(x1),x1),one)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(join(composition(converse(x1),x1),one),X) = join(converse(join(composition(converse(x1),x1),one)),X),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
composition(join(join(composition(converse(x1),x1),one),X3),X) = composition(join(converse(join(composition(converse(x1),x1),one)),X3),X),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
composition(join(converse(join(composition(converse(x1),x1),one)),X3),X) = join(composition(converse(join(composition(converse(x1),x1),one)),X),composition(X3,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c125,plain,
join(composition(converse(join(composition(converse(x1),x1),one)),X),composition(X3,X)) = join(X,composition(X3,X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c126,plain,
composition(join(converse(join(composition(converse(x1),x1),one)),X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
composition(join(join(composition(converse(x1),x1),one),X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c123,c126]) ).
cnf(c128,plain,
composition(join(X3,join(composition(converse(x1),x1),one)),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c98,c127]) ).
cnf(c129,plain,
composition(join(X,join(composition(converse(x1),x1),one)),X3) = join(X3,composition(X,X3)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
composition(join(join(composition(converse(x1),x1),one),X),X3) = join(X3,composition(X,X3)),
inference(transitivity,[status(thm)],[c95,c129]) ).
cnf(c131,plain,
composition(join(join(composition(converse(x1),x1),one),composition(converse(x0),x0)),X) = join(X,composition(composition(converse(x0),x0),X)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
join(X,composition(composition(converse(x0),x0),X)) = composition(join(join(composition(converse(x1),x1),one),composition(converse(x0),x0)),X),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
join(join(composition(converse(x1),x1),one),composition(converse(x0),x0)) = join(composition(converse(x0),x0),one),
inference(substitution,[status(thm)],[c13]) ).
cnf(c134,plain,
composition(join(join(composition(converse(x1),x1),one),composition(converse(x0),x0)),X) = composition(join(composition(converse(x0),x0),one),X),
inference(congruence,[status(thm)],[c133]) ).
fof(c135,conjecture,
! [X0_2,X1_2] :
( ( join(composition(converse(X0_2),X0_2),one) = one
& join(composition(converse(X1_2),X1_2),one) = one )
=> join(composition(converse(composition(X0_2,X1_2)),composition(X0_2,X1_2)),one) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c136,negated_conjecture,
~ ! [X0_2,X1_2] :
( ( join(composition(converse(X0_2),X0_2),one) = one
& join(composition(converse(X1_2),X1_2),one) = one )
=> join(composition(converse(composition(X0_2,X1_2)),composition(X0_2,X1_2)),one) = one ),
inference(negate_conjecture,[status(cth)],[c135]) ).
fof(c137,plain,
( join(composition(converse(x0),x0),one) = one
& join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) != one
& join(composition(converse(x1),x1),one) = one ),
inference(clausify,[status(esa)],[c136]) ).
cnf(c138,plain,
join(composition(converse(x0),x0),one) = one,
inference(clausify,[status(thm)],[c137]) ).
cnf(c139,plain,
one = join(composition(converse(x1),x1),one),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c140,plain,
join(composition(converse(x0),x0),one) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
composition(join(composition(converse(x0),x0),one),X) = composition(join(composition(converse(x1),x1),one),X),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
join(composition(converse(x1),x1),one) = converse(join(composition(converse(x1),x1),one)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c143,plain,
composition(join(composition(converse(x1),x1),one),X) = composition(converse(join(composition(converse(x1),x1),one)),X),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
composition(join(composition(converse(x1),x1),one),X) = X,
inference(transitivity,[status(thm)],[c143,c116]) ).
cnf(c145,plain,
composition(join(composition(converse(x0),x0),one),X) = X,
inference(transitivity,[status(thm)],[c141,c144]) ).
cnf(c146,plain,
composition(join(join(composition(converse(x1),x1),one),composition(converse(x0),x0)),X) = X,
inference(transitivity,[status(thm)],[c134,c145]) ).
cnf(c147,plain,
join(X,composition(composition(converse(x0),x0),X)) = X,
inference(transitivity,[status(thm)],[c132,c146]) ).
cnf(c148,plain,
composition(converse(X3),join(X,composition(composition(converse(x0),x0),X))) = composition(converse(X3),X),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
join(composition(converse(X3),X),composition(converse(X3),composition(composition(converse(x0),x0),X))) = composition(converse(X3),X),
inference(transitivity,[status(thm)],[c92,c148]) ).
cnf(c150,plain,
join(composition(converse(X3),X),composition(converse(composition(x0,X3)),composition(x0,X))) = composition(converse(X3),X),
inference(transitivity,[status(thm)],[c44,c149]) ).
cnf(c151,plain,
join(composition(converse(composition(x0,X3)),composition(x0,X)),composition(converse(X3),X)) = composition(converse(X3),X),
inference(transitivity,[status(thm)],[c31,c150]) ).
cnf(c152,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),composition(converse(x1),x1)) = composition(converse(x1),x1),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
join(join(composition(converse(x1),x1),one),join(composition(converse(composition(x0,x1)),composition(x0,x1)),composition(converse(x1),x1))) = join(join(composition(converse(x1),x1),one),composition(converse(x1),x1)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
join(join(composition(converse(x1),x1),one),composition(converse(x1),x1)) = join(composition(converse(x1),x1),one),
inference(substitution,[status(thm)],[c13]) ).
cnf(c155,plain,
join(join(composition(converse(x1),x1),one),join(composition(converse(composition(x0,x1)),composition(x0,x1)),composition(converse(x1),x1))) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c153,c154]) ).
cnf(c156,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),join(composition(converse(x1),x1),one)) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c29,c155]) ).
cnf(c157,plain,
join(join(composition(converse(x1),x1),one),composition(converse(composition(x0,x1)),composition(x0,x1))) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c17,c156]) ).
cnf(c158,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) = join(composition(converse(x1),x1),one),
inference(transitivity,[status(thm)],[c15,c157]) ).
cnf(c159,plain,
join(composition(converse(composition(x0,x1)),composition(x0,x1)),one) = one,
inference(transitivity,[status(thm)],[c158,c8]) ).
cnf(c160,plain,
$false,
inference(resolution,[status(thm)],[c4,c159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.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 22:54:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.39/0.60 Command-line arguments: --flatten --complete-subsets
% 1.39/0.60
% 1.39/0.60 % SZS status Theorem
% 1.39/0.60
% 1.39/0.61 % SZS output start CNFRefutation
% See solution above
% 1.83/0.70
% 1.83/0.70 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------