%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:33:22 PM UTC 2026
% Result : Unsatisfiable 0.75s 0.61s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of clauses : 153 ( 153 unt; 0 nHn; 32 RR)
% Number of literals : 153 ( 152 equ; 1 neg)
% Maximal clause size : 1 ( 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 : 234 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
cnf(c2,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c3,plain,
join(X,join(composition(converse(sk1),sk1),one)) = join(join(composition(converse(sk1),sk1),one),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(composition(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
join(X,join(composition(converse(sk1),sk1),one)) = join(X,one),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(X,one),
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) = join(join(composition(converse(sk1),sk1),one),composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),join(composition(converse(sk1),sk1),one)) = join(join(composition(converse(sk1),sk1),one),composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),join(composition(converse(sk1),sk1),one)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
join(composition(converse(sk2),sk2),X) = join(X,composition(converse(sk2),sk2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
join(X,composition(converse(sk2),sk2)) = join(composition(converse(sk2),sk2),X),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
join(join(composition(converse(sk1),sk1),one),join(X,composition(converse(sk2),sk2))) = join(join(composition(converse(sk1),sk1),one),join(composition(converse(sk2),sk2),X)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c16,plain,
join(join(composition(converse(sk1),sk1),one),join(composition(converse(sk2),sk2),X)) = join(join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)) = join(composition(converse(sk2),sk2),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c18,plain,
join(join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)),X) = join(join(composition(converse(sk2),sk2),one),X),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
join(composition(converse(sk2),sk2),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c20,plain,
one = join(composition(converse(sk1),sk1),one),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c21,plain,
join(composition(converse(sk2),sk2),one) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
join(join(composition(converse(sk2),sk2),one),X) = join(join(composition(converse(sk1),sk1),one),X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
join(join(composition(converse(sk2),sk2),one),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
join(join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(transitivity,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
join(join(composition(converse(sk1),sk1),one),join(composition(converse(sk2),sk2),X)) = join(X,join(composition(converse(sk1),sk1),one)),
inference(transitivity,[status(thm)],[c16,c25]) ).
cnf(c27,plain,
join(join(composition(converse(sk1),sk1),one),join(X,composition(converse(sk2),sk2))) = join(X,join(composition(converse(sk1),sk1),one)),
inference(transitivity,[status(thm)],[c14,c26]) ).
cnf(c28,plain,
join(join(composition(converse(sk1),sk1),one),join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),composition(converse(sk2),sk2))) = join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),join(composition(converse(sk1),sk1),one)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),join(composition(converse(sk1),sk1),one)) = join(join(composition(converse(sk1),sk1),one),join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),composition(converse(sk2),sk2))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
join(composition(converse(X),X2),composition(converse(composition(sk1,X)),composition(sk1,X2))) = join(composition(converse(composition(sk1,X)),composition(sk1,X2)),composition(converse(X),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
join(composition(converse(composition(sk1,X2)),composition(sk1,X)),composition(converse(X2),X)) = join(composition(converse(X2),X),composition(converse(composition(sk1,X2)),composition(sk1,X))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c33,plain,
converse(composition(X,X2)) = composition(converse(X2),converse(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
composition(converse(composition(X,X2)),X3) = composition(composition(converse(X2),converse(X)),X3),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c36,plain,
composition(converse(X3),composition(converse(X2),X)) = composition(composition(converse(X3),converse(X2)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
composition(composition(converse(X3),converse(X2)),X) = composition(converse(X3),composition(converse(X2),X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
composition(converse(composition(X2,X3)),X) = composition(converse(X3),composition(converse(X2),X)),
inference(transitivity,[status(thm)],[c34,c37]) ).
cnf(c39,plain,
composition(converse(composition(X2,X3)),composition(X,X4)) = composition(converse(X3),composition(converse(X2),composition(X,X4))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
composition(converse(X3),composition(X2,X)) = composition(composition(converse(X3),X2),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c41,plain,
composition(converse(X4),composition(converse(X3),composition(X2,X))) = composition(converse(X4),composition(composition(converse(X3),X2),X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
composition(converse(composition(X3,X4)),composition(X2,X)) = composition(converse(X4),composition(composition(converse(X3),X2),X)),
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
composition(converse(composition(sk1,X2)),composition(sk1,X)) = composition(converse(X2),composition(composition(converse(sk1),sk1),X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
join(composition(converse(X2),X),composition(converse(composition(sk1,X2)),composition(sk1,X))) = join(composition(converse(X2),X),composition(converse(X2),composition(composition(converse(sk1),sk1),X))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
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(X2),X) = composition(converse(X2),converse(converse(X))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
join(composition(converse(X3),X2),composition(converse(X3),X)) = join(composition(converse(X3),X2),composition(converse(X3),converse(converse(X)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
converse(composition(X,X2)) = composition(converse(X2),converse(X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c51,plain,
composition(converse(X2),converse(X)) = converse(composition(X,X2)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
join(composition(converse(X3),X2),composition(converse(X3),converse(X))) = join(composition(converse(X3),X2),converse(composition(X,X3))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
converse(composition(converse(X2),X)) = composition(converse(X),converse(converse(X2))),
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(X2))) = composition(converse(X),X2),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
converse(composition(converse(X2),X)) = composition(converse(X),X2),
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
converse(composition(converse(X),X2)) = composition(converse(X2),X),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
composition(converse(X2),X) = converse(composition(converse(X),X2)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
join(composition(converse(X3),X2),converse(composition(X,X3))) = join(converse(composition(converse(X2),X3)),converse(composition(X,X3))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c61,plain,
converse(join(composition(converse(X2),X3),composition(X,X3))) = join(converse(composition(converse(X2),X3)),converse(composition(X,X3))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
join(converse(composition(converse(X2),X3)),converse(composition(X,X3))) = converse(join(composition(converse(X2),X3),composition(X,X3))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c64,plain,
composition(join(X2,X3),X) = join(composition(X2,X),composition(X3,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
join(composition(X2,X),composition(X3,X)) = composition(join(X2,X3),X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
composition(join(X2,X3),X) = composition(join(X3,X2),X),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
join(composition(X2,X),composition(X3,X)) = composition(join(X3,X2),X),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
join(composition(converse(X2),X3),composition(X,X3)) = composition(join(X,converse(X2)),X3),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
converse(join(composition(converse(X2),X3),composition(X,X3))) = converse(composition(join(X,converse(X2)),X3)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
converse(composition(join(X,converse(X2)),X3)) = composition(converse(X3),converse(join(X,converse(X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c72,plain,
converse(join(X,converse(X2))) = join(converse(X),converse(converse(X2))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c73,plain,
composition(converse(X3),converse(join(X,converse(X2)))) = composition(converse(X3),join(converse(X),converse(converse(X2)))),
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(X2))) = join(converse(X),X2),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
composition(converse(X3),join(converse(X),converse(converse(X2)))) = composition(converse(X3),join(converse(X),X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
join(converse(X),X2) = join(X2,converse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
composition(converse(X3),join(converse(X),X2)) = composition(converse(X3),join(X2,converse(X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
composition(converse(X3),join(converse(X),converse(converse(X2)))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
composition(converse(X3),converse(join(X,converse(X2)))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c73,c79]) ).
cnf(c81,plain,
converse(composition(join(X,converse(X2)),X3)) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c71,c80]) ).
cnf(c82,plain,
converse(join(composition(converse(X2),X3),composition(X,X3))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c70,c81]) ).
cnf(c83,plain,
join(converse(composition(converse(X2),X3)),converse(composition(X,X3))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c62,c82]) ).
cnf(c84,plain,
join(composition(converse(X3),X2),converse(composition(X,X3))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c59,c83]) ).
cnf(c85,plain,
join(composition(converse(X3),X2),composition(converse(X3),converse(X))) = composition(converse(X3),join(X2,converse(X))),
inference(transitivity,[status(thm)],[c52,c84]) ).
cnf(c86,plain,
join(composition(converse(X3),X2),composition(converse(X3),converse(converse(X)))) = composition(converse(X3),join(X2,converse(converse(X)))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c88,plain,
join(X2,converse(converse(X))) = join(X2,X),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
composition(converse(X3),join(X2,converse(converse(X)))) = composition(converse(X3),join(X2,X)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
join(composition(converse(X3),X2),composition(converse(X3),converse(converse(X)))) = composition(converse(X3),join(X2,X)),
inference(transitivity,[status(thm)],[c86,c89]) ).
cnf(c91,plain,
join(composition(converse(X3),X2),composition(converse(X3),X)) = composition(converse(X3),join(X2,X)),
inference(transitivity,[status(thm)],[c49,c90]) ).
cnf(c92,plain,
join(composition(converse(X2),X),composition(converse(X2),composition(composition(converse(sk1),sk1),X))) = composition(converse(X2),join(X,composition(composition(converse(sk1),sk1),X))),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
join(X,join(composition(converse(sk1),sk1),one)) = join(join(composition(converse(sk1),sk1),one),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
composition(join(join(composition(converse(sk1),sk1),one),X),X2) = composition(join(X,join(composition(converse(sk1),sk1),one)),X2),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(X,join(composition(converse(sk1),sk1),one)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c97,plain,
join(X,join(composition(converse(sk1),sk1),one)) = join(join(composition(converse(sk1),sk1),one),X),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
composition(join(X2,join(composition(converse(sk1),sk1),one)),X) = composition(join(join(composition(converse(sk1),sk1),one),X2),X),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c100,plain,
composition(converse(join(composition(converse(sk1),sk1),one)),one) = converse(join(composition(converse(sk1),sk1),one)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
converse(join(composition(converse(sk1),sk1),one)) = composition(converse(join(composition(converse(sk1),sk1),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(sk1),sk1),one)),X) = composition(converse(join(composition(converse(sk1),sk1),one)),converse(converse(X))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
converse(join(composition(converse(sk1),sk1),one)) = converse(one),
inference(congruence,[status(thm)],[c5]) ).
cnf(c106,plain,
composition(converse(join(composition(converse(sk1),sk1),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(sk1),sk1),one)),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c106,c111]) ).
cnf(c113,plain,
composition(converse(join(composition(converse(sk1),sk1),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(sk1),sk1),one)),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
composition(converse(join(composition(converse(sk1),sk1),one)),X) = X,
inference(transitivity,[status(thm)],[c104,c115]) ).
cnf(c117,plain,
composition(converse(join(composition(converse(sk1),sk1),one)),one) = one,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
one = join(composition(converse(sk1),sk1),one),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c119,plain,
composition(converse(join(composition(converse(sk1),sk1),one)),one) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
converse(join(composition(converse(sk1),sk1),one)) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c101,c119]) ).
cnf(c121,plain,
join(composition(converse(sk1),sk1),one) = converse(join(composition(converse(sk1),sk1),one)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(join(composition(converse(sk1),sk1),one),X) = join(converse(join(composition(converse(sk1),sk1),one)),X),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
composition(join(join(composition(converse(sk1),sk1),one),X2),X) = composition(join(converse(join(composition(converse(sk1),sk1),one)),X2),X),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
composition(join(converse(join(composition(converse(sk1),sk1),one)),X2),X) = join(composition(converse(join(composition(converse(sk1),sk1),one)),X),composition(X2,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c125,plain,
join(composition(converse(join(composition(converse(sk1),sk1),one)),X),composition(X2,X)) = join(X,composition(X2,X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c126,plain,
composition(join(converse(join(composition(converse(sk1),sk1),one)),X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
composition(join(join(composition(converse(sk1),sk1),one),X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c123,c126]) ).
cnf(c128,plain,
composition(join(X2,join(composition(converse(sk1),sk1),one)),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c98,c127]) ).
cnf(c129,plain,
composition(join(X,join(composition(converse(sk1),sk1),one)),X2) = join(X2,composition(X,X2)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
composition(join(join(composition(converse(sk1),sk1),one),X),X2) = join(X2,composition(X,X2)),
inference(transitivity,[status(thm)],[c95,c129]) ).
cnf(c131,plain,
composition(join(join(composition(converse(sk1),sk1),one),composition(converse(sk1),sk1)),X) = join(X,composition(composition(converse(sk1),sk1),X)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
join(X,composition(composition(converse(sk1),sk1),X)) = composition(join(join(composition(converse(sk1),sk1),one),composition(converse(sk1),sk1)),X),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(sk1),sk1)) = join(composition(converse(sk1),sk1),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c134,plain,
composition(join(join(composition(converse(sk1),sk1),one),composition(converse(sk1),sk1)),X) = composition(join(composition(converse(sk1),sk1),one),X),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
join(composition(converse(sk1),sk1),one) = converse(join(composition(converse(sk1),sk1),one)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c136,plain,
composition(join(composition(converse(sk1),sk1),one),X) = composition(converse(join(composition(converse(sk1),sk1),one)),X),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
composition(join(composition(converse(sk1),sk1),one),X) = X,
inference(transitivity,[status(thm)],[c136,c116]) ).
cnf(c138,plain,
composition(join(join(composition(converse(sk1),sk1),one),composition(converse(sk1),sk1)),X) = X,
inference(transitivity,[status(thm)],[c134,c137]) ).
cnf(c139,plain,
join(X,composition(composition(converse(sk1),sk1),X)) = X,
inference(transitivity,[status(thm)],[c132,c138]) ).
cnf(c140,plain,
composition(converse(X2),join(X,composition(composition(converse(sk1),sk1),X))) = composition(converse(X2),X),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
join(composition(converse(X2),X),composition(converse(X2),composition(composition(converse(sk1),sk1),X))) = composition(converse(X2),X),
inference(transitivity,[status(thm)],[c92,c140]) ).
cnf(c142,plain,
join(composition(converse(X2),X),composition(converse(composition(sk1,X2)),composition(sk1,X))) = composition(converse(X2),X),
inference(transitivity,[status(thm)],[c44,c141]) ).
cnf(c143,plain,
join(composition(converse(composition(sk1,X2)),composition(sk1,X)),composition(converse(X2),X)) = composition(converse(X2),X),
inference(transitivity,[status(thm)],[c31,c142]) ).
cnf(c144,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),composition(converse(sk2),sk2)) = composition(converse(sk2),sk2),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
join(join(composition(converse(sk1),sk1),one),join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),composition(converse(sk2),sk2))) = join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)) = join(composition(converse(sk2),sk2),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c147,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(sk2),sk2)) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c146,c21]) ).
cnf(c148,plain,
join(join(composition(converse(sk1),sk1),one),join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),composition(converse(sk2),sk2))) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c145,c147]) ).
cnf(c149,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),join(composition(converse(sk1),sk1),one)) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c29,c148]) ).
cnf(c150,plain,
join(join(composition(converse(sk1),sk1),one),composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c11,c149]) ).
cnf(c151,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) = join(composition(converse(sk1),sk1),one),
inference(transitivity,[status(thm)],[c9,c150]) ).
cnf(c152,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) = one,
inference(transitivity,[status(thm)],[c151,c5]) ).
cnf(c153,plain,
$false,
inference(resolution,[status(thm)],[c1,c152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 22:54:04 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.61 Command-line arguments: --flatten --complete-subsets
% 0.75/0.61
% 0.75/0.61 % SZS status Unsatisfiable
% 0.75/0.61
% 0.75/0.62 % SZS output start CNFRefutation
% See solution above
% 1.81/0.69
% 1.81/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------