%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:33:34 PM UTC 2026
% Result : Theorem 0.79s 0.52s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:59:56 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/0.52 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.79/0.52
% 0.79/0.52 % SZS status Theorem
% 0.79/0.52
% 0.79/0.54 % SZS output start Proof
% 0.79/0.55 Axiom 1 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.79/0.55 Axiom 2 (def_top): top = join(X, complement(X)).
% 0.79/0.55 Axiom 3 (composition_identity): composition(X, one) = X.
% 0.79/0.55 Axiom 4 (converse_idempotence): converse(converse(X)) = X.
% 0.79/0.55 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 0.79/0.55 Axiom 6 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.79/0.55 Axiom 7 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.79/0.55 Axiom 8 (goals): join(join(x0, x1), x2) = x2.
% 0.79/0.55 Axiom 9 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.79/0.55 Axiom 10 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.79/0.55 Axiom 11 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.79/0.55 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.79/0.55
% 0.79/0.55 Lemma 13: complement(top) = zero.
% 0.79/0.55 Proof:
% 0.79/0.55 complement(top)
% 0.79/0.55 = { by axiom 2 (def_top) }
% 0.79/0.55 complement(join(complement(X), complement(complement(X))))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 0.79/0.55 meet(X, complement(X))
% 0.79/0.55 = { by axiom 5 (def_zero) R->L }
% 0.79/0.55 zero
% 0.79/0.55
% 0.79/0.55 Lemma 14: meet(Y, X) = meet(X, Y).
% 0.79/0.55 Proof:
% 0.79/0.55 meet(Y, X)
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) }
% 0.79/0.55 complement(join(complement(Y), complement(X)))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 complement(join(complement(X), complement(Y)))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 0.79/0.55 meet(X, Y)
% 0.79/0.55
% 0.79/0.55 Lemma 15: complement(join(zero, complement(X))) = meet(X, top).
% 0.79/0.55 Proof:
% 0.79/0.55 complement(join(zero, complement(X)))
% 0.79/0.55 = { by lemma 13 R->L }
% 0.79/0.55 complement(join(complement(top), complement(X)))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 0.79/0.55 meet(top, X)
% 0.79/0.55 = { by lemma 14 R->L }
% 0.79/0.55 meet(X, top)
% 0.79/0.55
% 0.79/0.55 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 0.79/0.55 Proof:
% 0.79/0.55 join(X, join(Y, complement(X)))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(X, join(complement(X), Y))
% 0.79/0.55 = { by axiom 7 (maddux2_join_associativity) }
% 0.79/0.55 join(join(X, complement(X)), Y)
% 0.79/0.55 = { by axiom 2 (def_top) R->L }
% 0.79/0.55 join(top, Y)
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) }
% 0.79/0.55 join(Y, top)
% 0.79/0.55
% 0.79/0.55 Lemma 17: composition(converse(one), X) = X.
% 0.79/0.55 Proof:
% 0.79/0.55 composition(converse(one), X)
% 0.79/0.55 = { by axiom 4 (converse_idempotence) R->L }
% 0.79/0.55 composition(converse(one), converse(converse(X)))
% 0.79/0.55 = { by axiom 9 (converse_multiplicativity) R->L }
% 0.79/0.55 converse(composition(converse(X), one))
% 0.79/0.55 = { by axiom 3 (composition_identity) }
% 0.79/0.55 converse(converse(X))
% 0.79/0.55 = { by axiom 4 (converse_idempotence) }
% 0.79/0.55 X
% 0.79/0.55
% 0.79/0.55 Lemma 18: join(complement(X), complement(X)) = complement(X).
% 0.79/0.55 Proof:
% 0.79/0.55 join(complement(X), complement(X))
% 0.79/0.55 = { by lemma 17 R->L }
% 0.79/0.55 join(complement(X), composition(converse(one), complement(X)))
% 0.79/0.55 = { by lemma 17 R->L }
% 0.79/0.55 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.79/0.55 = { by axiom 3 (composition_identity) R->L }
% 0.79/0.55 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.79/0.55 = { by axiom 10 (composition_associativity) R->L }
% 0.79/0.55 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.79/0.55 = { by lemma 17 }
% 0.79/0.55 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.79/0.55 = { by axiom 12 (converse_cancellativity) }
% 0.79/0.55 complement(X)
% 0.79/0.55
% 0.79/0.55 Lemma 19: join(top, complement(X)) = top.
% 0.79/0.55 Proof:
% 0.79/0.55 join(top, complement(X))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(complement(X), top)
% 0.79/0.55 = { by lemma 16 R->L }
% 0.79/0.55 join(X, join(complement(X), complement(X)))
% 0.79/0.55 = { by lemma 18 }
% 0.79/0.55 join(X, complement(X))
% 0.79/0.55 = { by axiom 2 (def_top) R->L }
% 0.79/0.55 top
% 0.79/0.55
% 0.79/0.55 Lemma 20: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.79/0.55 Proof:
% 0.79/0.55 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) }
% 0.79/0.55 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.79/0.55 = { by axiom 11 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.79/0.55 X
% 0.79/0.55
% 0.79/0.55 Lemma 21: join(zero, meet(X, top)) = X.
% 0.79/0.55 Proof:
% 0.79/0.55 join(zero, meet(X, top))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(meet(X, top), zero)
% 0.79/0.55 = { by lemma 13 R->L }
% 0.79/0.55 join(meet(X, top), complement(top))
% 0.79/0.55 = { by lemma 19 R->L }
% 0.79/0.55 join(meet(X, top), complement(join(top, complement(zero))))
% 0.79/0.55 = { by axiom 2 (def_top) }
% 0.79/0.55 join(meet(X, top), complement(join(join(top, complement(top)), complement(zero))))
% 0.79/0.55 = { by lemma 13 }
% 0.79/0.55 join(meet(X, top), complement(join(join(top, zero), complement(zero))))
% 0.79/0.55 = { by axiom 7 (maddux2_join_associativity) R->L }
% 0.79/0.55 join(meet(X, top), complement(join(top, join(zero, complement(zero)))))
% 0.79/0.55 = { by axiom 2 (def_top) R->L }
% 0.79/0.55 join(meet(X, top), complement(join(top, top)))
% 0.79/0.55 = { by lemma 16 R->L }
% 0.79/0.55 join(meet(X, top), complement(join(complement(X), join(top, complement(complement(X))))))
% 0.79/0.55 = { by lemma 19 }
% 0.79/0.55 join(meet(X, top), complement(join(complement(X), top)))
% 0.79/0.55 = { by lemma 20 }
% 0.79/0.55 X
% 0.79/0.55
% 0.79/0.55 Lemma 22: meet(X, top) = X.
% 0.79/0.55 Proof:
% 0.79/0.55 meet(X, top)
% 0.79/0.55 = { by lemma 15 R->L }
% 0.79/0.55 complement(join(zero, complement(X)))
% 0.79/0.55 = { by lemma 21 R->L }
% 0.79/0.55 join(zero, meet(complement(join(zero, complement(X))), top))
% 0.79/0.55 = { by lemma 15 R->L }
% 0.79/0.55 join(zero, complement(join(zero, complement(complement(join(zero, complement(X)))))))
% 0.79/0.55 = { by axiom 5 (def_zero) }
% 0.79/0.55 join(zero, complement(join(meet(join(zero, complement(X)), complement(join(zero, complement(X)))), complement(complement(join(zero, complement(X)))))))
% 0.79/0.55 = { by lemma 18 R->L }
% 0.79/0.55 join(zero, complement(join(meet(join(zero, complement(X)), complement(join(zero, complement(X)))), complement(join(complement(join(zero, complement(X))), complement(join(zero, complement(X))))))))
% 0.79/0.55 = { by lemma 20 }
% 0.79/0.55 join(zero, complement(join(zero, complement(X))))
% 0.79/0.55 = { by lemma 15 }
% 0.79/0.55 join(zero, meet(X, top))
% 0.79/0.55 = { by lemma 21 }
% 0.79/0.55 X
% 0.79/0.55
% 0.79/0.55 Lemma 23: join(X, X) = X.
% 0.79/0.55 Proof:
% 0.79/0.55 join(X, X)
% 0.79/0.55 = { by lemma 22 R->L }
% 0.79/0.55 join(X, meet(X, top))
% 0.79/0.55 = { by lemma 22 R->L }
% 0.79/0.55 join(meet(X, top), meet(X, top))
% 0.79/0.55 = { by lemma 14 }
% 0.79/0.55 join(meet(top, X), meet(X, top))
% 0.79/0.55 = { by lemma 14 }
% 0.79/0.55 join(meet(top, X), meet(top, X))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) }
% 0.79/0.55 join(meet(top, X), complement(join(complement(top), complement(X))))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) }
% 0.79/0.55 join(complement(join(complement(top), complement(X))), complement(join(complement(top), complement(X))))
% 0.79/0.55 = { by lemma 18 }
% 0.79/0.55 complement(join(complement(top), complement(X)))
% 0.79/0.55 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 0.79/0.55 meet(top, X)
% 0.79/0.55 = { by lemma 14 R->L }
% 0.79/0.55 meet(X, top)
% 0.79/0.55 = { by lemma 22 }
% 0.79/0.55 X
% 0.79/0.55
% 0.79/0.55 Lemma 24: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 0.79/0.55 Proof:
% 0.79/0.55 join(Y, join(Z, X))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(join(Z, X), Y)
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) }
% 0.79/0.55 join(join(X, Z), Y)
% 0.79/0.55 = { by axiom 7 (maddux2_join_associativity) R->L }
% 0.79/0.55 join(X, join(Z, Y))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) }
% 0.79/0.55 join(X, join(Y, Z))
% 0.79/0.55
% 0.79/0.55 Lemma 25: join(X, join(X, Y)) = join(X, Y).
% 0.79/0.55 Proof:
% 0.79/0.55 join(X, join(X, Y))
% 0.79/0.55 = { by lemma 24 }
% 0.79/0.55 join(Y, join(X, X))
% 0.79/0.55 = { by lemma 23 }
% 0.79/0.55 join(Y, X)
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.55 join(X, Y)
% 0.79/0.55
% 0.79/0.55 Lemma 26: join(Z, join(Y, X)) = join(X, join(Y, Z)).
% 0.79/0.55 Proof:
% 0.79/0.55 join(Z, join(Y, X))
% 0.79/0.55 = { by lemma 24 }
% 0.79/0.55 join(X, join(Z, Y))
% 0.79/0.55 = { by axiom 1 (maddux1_join_commutativity) }
% 0.79/0.55 join(X, join(Y, Z))
% 0.79/0.55
% 0.79/0.55 Lemma 27: join(x0, join(x1, x2)) = x2.
% 0.79/0.55 Proof:
% 0.79/0.55 join(x0, join(x1, x2))
% 0.79/0.55 = { by axiom 7 (maddux2_join_associativity) }
% 0.79/0.55 join(join(x0, x1), x2)
% 0.79/0.55 = { by axiom 8 (goals) }
% 0.79/0.55 x2
% 0.79/0.55
% 0.79/0.55 Lemma 28: join(x1, join(x0, x2)) = x2.
% 0.79/0.55 Proof:
% 0.79/0.55 join(x1, join(x0, x2))
% 0.79/0.55 = { by lemma 26 }
% 0.79/0.55 join(x2, join(x0, x1))
% 0.79/0.55 = { by lemma 24 R->L }
% 0.79/0.55 join(x0, join(x1, x2))
% 0.79/0.55 = { by lemma 27 }
% 0.79/0.55 x2
% 0.79/0.55
% 0.79/0.55 Goal 1 (goals_1): tuple(join(x0, x2), join(x1, x2)) = tuple(x2, x2).
% 0.79/0.56 Proof:
% 0.79/0.56 tuple(join(x0, x2), join(x1, x2))
% 0.79/0.56 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.79/0.56 tuple(join(x0, x2), join(x2, x1))
% 0.79/0.56 = { by lemma 27 R->L }
% 0.79/0.56 tuple(join(x0, x2), join(join(x0, join(x1, x2)), x1))
% 0.79/0.56 = { by axiom 7 (maddux2_join_associativity) R->L }
% 0.79/0.56 tuple(join(x0, x2), join(x0, join(join(x1, x2), x1)))
% 0.79/0.56 = { by axiom 1 (maddux1_join_commutativity) }
% 0.79/0.56 tuple(join(x0, x2), join(x0, join(x1, join(x1, x2))))
% 0.79/0.56 = { by lemma 25 }
% 0.79/0.56 tuple(join(x0, x2), join(x0, join(x1, x2)))
% 0.79/0.56 = { by lemma 27 }
% 0.79/0.56 tuple(join(x0, x2), x2)
% 0.79/0.56 = { by lemma 23 R->L }
% 0.79/0.56 tuple(join(join(x0, x2), join(x0, x2)), x2)
% 0.79/0.56 = { by lemma 26 }
% 0.79/0.56 tuple(join(x2, join(x0, join(x0, x2))), x2)
% 0.79/0.56 = { by lemma 25 }
% 0.79/0.56 tuple(join(x2, join(x0, x2)), x2)
% 0.79/0.56 = { by lemma 28 R->L }
% 0.79/0.56 tuple(join(join(x1, join(x0, x2)), join(x0, x2)), x2)
% 0.79/0.56 = { by axiom 7 (maddux2_join_associativity) R->L }
% 0.79/0.56 tuple(join(x1, join(join(x0, x2), join(x0, x2))), x2)
% 0.79/0.56 = { by lemma 23 }
% 0.79/0.56 tuple(join(x1, join(x0, x2)), x2)
% 0.79/0.56 = { by lemma 28 }
% 0.79/0.56 tuple(x2, x2)
% 0.79/0.56 % SZS output end Proof
% 0.79/0.56
% 0.79/0.56 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------