%------------------------------------------------------------------------------
% 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 : n020.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 : Unsatisfiable 0.97s 0.66s
% Output : Proof 1.49s
% 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.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n020.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 27 22:57:49 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.16/0.40 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.97/0.66 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.97/0.66
% 0.97/0.66 % SZS status Unsatisfiable
% 0.97/0.66
% 1.49/0.68 % SZS output start Proof
% 1.49/0.68 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 1.49/0.68 Axiom 2 (def_top_12): top = join(X, complement(X)).
% 1.49/0.68 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 1.49/0.68 Axiom 4 (converse_idempotence_8): converse(converse(X)) = X.
% 1.49/0.68 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 1.49/0.68 Axiom 6 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 1.49/0.68 Axiom 7 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 1.49/0.68 Axiom 8 (goals_14): join(join(sk1, sk2), sk3) = sk3.
% 1.49/0.68 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 1.49/0.68 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 1.49/0.68 Axiom 11 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 1.49/0.68 Axiom 12 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 1.49/0.68
% 1.49/0.68 Lemma 13: complement(top) = zero.
% 1.49/0.68 Proof:
% 1.49/0.68 complement(top)
% 1.49/0.68 = { by axiom 2 (def_top_12) }
% 1.49/0.68 complement(join(complement(X), complement(complement(X))))
% 1.49/0.68 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 1.49/0.68 meet(X, complement(X))
% 1.49/0.68 = { by axiom 5 (def_zero_13) R->L }
% 1.49/0.68 zero
% 1.49/0.68
% 1.49/0.68 Lemma 14: meet(Y, X) = meet(X, Y).
% 1.49/0.68 Proof:
% 1.49/0.68 meet(Y, X)
% 1.49/0.68 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 1.49/0.68 complement(join(complement(Y), complement(X)))
% 1.49/0.68 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.68 complement(join(complement(X), complement(Y)))
% 1.49/0.68 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 1.49/0.68 meet(X, Y)
% 1.49/0.68
% 1.49/0.68 Lemma 15: complement(join(zero, complement(X))) = meet(X, top).
% 1.49/0.68 Proof:
% 1.49/0.68 complement(join(zero, complement(X)))
% 1.49/0.68 = { by lemma 13 R->L }
% 1.49/0.68 complement(join(complement(top), complement(X)))
% 1.49/0.68 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 1.49/0.68 meet(top, X)
% 1.49/0.68 = { by lemma 14 R->L }
% 1.49/0.68 meet(X, top)
% 1.49/0.68
% 1.49/0.68 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 1.49/0.68 Proof:
% 1.49/0.68 join(X, join(Y, complement(X)))
% 1.49/0.68 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.68 join(X, join(complement(X), Y))
% 1.49/0.68 = { by axiom 7 (maddux2_join_associativity_2) }
% 1.49/0.68 join(join(X, complement(X)), Y)
% 1.49/0.68 = { by axiom 2 (def_top_12) R->L }
% 1.49/0.68 join(top, Y)
% 1.49/0.68 = { by axiom 1 (maddux1_join_commutativity_1) }
% 1.49/0.68 join(Y, top)
% 1.49/0.68
% 1.49/0.68 Lemma 17: composition(converse(one), X) = X.
% 1.49/0.68 Proof:
% 1.49/0.68 composition(converse(one), X)
% 1.49/0.68 = { by axiom 4 (converse_idempotence_8) R->L }
% 1.49/0.68 composition(converse(one), converse(converse(X)))
% 1.49/0.68 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 1.49/0.68 converse(composition(converse(X), one))
% 1.49/0.68 = { by axiom 3 (composition_identity_6) }
% 1.49/0.68 converse(converse(X))
% 1.49/0.68 = { by axiom 4 (converse_idempotence_8) }
% 1.49/0.69 X
% 1.49/0.69
% 1.49/0.69 Lemma 18: join(complement(X), complement(X)) = complement(X).
% 1.49/0.69 Proof:
% 1.49/0.69 join(complement(X), complement(X))
% 1.49/0.69 = { by lemma 17 R->L }
% 1.49/0.69 join(complement(X), composition(converse(one), complement(X)))
% 1.49/0.69 = { by lemma 17 R->L }
% 1.49/0.69 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 1.49/0.69 = { by axiom 3 (composition_identity_6) R->L }
% 1.49/0.69 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 1.49/0.69 = { by axiom 10 (composition_associativity_5) R->L }
% 1.49/0.69 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 1.49/0.69 = { by lemma 17 }
% 1.49/0.69 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 1.49/0.69 = { by axiom 12 (converse_cancellativity_11) }
% 1.49/0.69 complement(X)
% 1.49/0.69
% 1.49/0.69 Lemma 19: join(top, complement(X)) = top.
% 1.49/0.69 Proof:
% 1.49/0.69 join(top, complement(X))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 join(complement(X), top)
% 1.49/0.69 = { by lemma 16 R->L }
% 1.49/0.69 join(X, join(complement(X), complement(X)))
% 1.49/0.69 = { by lemma 18 }
% 1.49/0.69 join(X, complement(X))
% 1.49/0.69 = { by axiom 2 (def_top_12) R->L }
% 1.49/0.69 top
% 1.49/0.69
% 1.49/0.69 Lemma 20: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 1.49/0.69 Proof:
% 1.49/0.69 join(meet(X, Y), complement(join(complement(X), Y)))
% 1.49/0.69 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 1.49/0.69 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 1.49/0.69 = { by axiom 11 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 1.49/0.69 X
% 1.49/0.69
% 1.49/0.69 Lemma 21: join(zero, meet(X, top)) = X.
% 1.49/0.69 Proof:
% 1.49/0.69 join(zero, meet(X, top))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 join(meet(X, top), zero)
% 1.49/0.69 = { by lemma 13 R->L }
% 1.49/0.69 join(meet(X, top), complement(top))
% 1.49/0.69 = { by lemma 19 R->L }
% 1.49/0.69 join(meet(X, top), complement(join(top, complement(zero))))
% 1.49/0.69 = { by axiom 2 (def_top_12) }
% 1.49/0.69 join(meet(X, top), complement(join(join(top, complement(top)), complement(zero))))
% 1.49/0.69 = { by lemma 13 }
% 1.49/0.69 join(meet(X, top), complement(join(join(top, zero), complement(zero))))
% 1.49/0.69 = { by axiom 7 (maddux2_join_associativity_2) R->L }
% 1.49/0.69 join(meet(X, top), complement(join(top, join(zero, complement(zero)))))
% 1.49/0.69 = { by axiom 2 (def_top_12) R->L }
% 1.49/0.69 join(meet(X, top), complement(join(top, top)))
% 1.49/0.69 = { by lemma 16 R->L }
% 1.49/0.69 join(meet(X, top), complement(join(complement(X), join(top, complement(complement(X))))))
% 1.49/0.69 = { by lemma 19 }
% 1.49/0.69 join(meet(X, top), complement(join(complement(X), top)))
% 1.49/0.69 = { by lemma 20 }
% 1.49/0.69 X
% 1.49/0.69
% 1.49/0.69 Lemma 22: meet(X, top) = X.
% 1.49/0.69 Proof:
% 1.49/0.69 meet(X, top)
% 1.49/0.69 = { by lemma 15 R->L }
% 1.49/0.69 complement(join(zero, complement(X)))
% 1.49/0.69 = { by lemma 21 R->L }
% 1.49/0.69 join(zero, meet(complement(join(zero, complement(X))), top))
% 1.49/0.69 = { by lemma 15 R->L }
% 1.49/0.69 join(zero, complement(join(zero, complement(complement(join(zero, complement(X)))))))
% 1.49/0.69 = { by axiom 5 (def_zero_13) }
% 1.49/0.69 join(zero, complement(join(meet(join(zero, complement(X)), complement(join(zero, complement(X)))), complement(complement(join(zero, complement(X)))))))
% 1.49/0.69 = { by lemma 18 R->L }
% 1.49/0.69 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))))))))
% 1.49/0.69 = { by lemma 20 }
% 1.49/0.69 join(zero, complement(join(zero, complement(X))))
% 1.49/0.69 = { by lemma 15 }
% 1.49/0.69 join(zero, meet(X, top))
% 1.49/0.69 = { by lemma 21 }
% 1.49/0.69 X
% 1.49/0.69
% 1.49/0.69 Lemma 23: join(X, X) = X.
% 1.49/0.69 Proof:
% 1.49/0.69 join(X, X)
% 1.49/0.69 = { by lemma 22 R->L }
% 1.49/0.69 join(X, meet(X, top))
% 1.49/0.69 = { by lemma 22 R->L }
% 1.49/0.69 join(meet(X, top), meet(X, top))
% 1.49/0.69 = { by lemma 14 }
% 1.49/0.69 join(meet(top, X), meet(X, top))
% 1.49/0.69 = { by lemma 14 }
% 1.49/0.69 join(meet(top, X), meet(top, X))
% 1.49/0.69 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 1.49/0.69 join(meet(top, X), complement(join(complement(top), complement(X))))
% 1.49/0.69 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 1.49/0.69 join(complement(join(complement(top), complement(X))), complement(join(complement(top), complement(X))))
% 1.49/0.69 = { by lemma 18 }
% 1.49/0.69 complement(join(complement(top), complement(X)))
% 1.49/0.69 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 1.49/0.69 meet(top, X)
% 1.49/0.69 = { by lemma 14 R->L }
% 1.49/0.69 meet(X, top)
% 1.49/0.69 = { by lemma 22 }
% 1.49/0.69 X
% 1.49/0.69
% 1.49/0.69 Lemma 24: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 1.49/0.69 Proof:
% 1.49/0.69 join(Y, join(Z, X))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 join(join(Z, X), Y)
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) }
% 1.49/0.69 join(join(X, Z), Y)
% 1.49/0.69 = { by axiom 7 (maddux2_join_associativity_2) R->L }
% 1.49/0.69 join(X, join(Z, Y))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) }
% 1.49/0.69 join(X, join(Y, Z))
% 1.49/0.69
% 1.49/0.69 Lemma 25: join(X, join(X, Y)) = join(X, Y).
% 1.49/0.69 Proof:
% 1.49/0.69 join(X, join(X, Y))
% 1.49/0.69 = { by lemma 24 }
% 1.49/0.69 join(Y, join(X, X))
% 1.49/0.69 = { by lemma 23 }
% 1.49/0.69 join(Y, X)
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 join(X, Y)
% 1.49/0.69
% 1.49/0.69 Lemma 26: join(Z, join(Y, X)) = join(X, join(Y, Z)).
% 1.49/0.69 Proof:
% 1.49/0.69 join(Z, join(Y, X))
% 1.49/0.69 = { by lemma 24 }
% 1.49/0.69 join(X, join(Z, Y))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) }
% 1.49/0.69 join(X, join(Y, Z))
% 1.49/0.69
% 1.49/0.69 Lemma 27: join(sk1, join(sk2, sk3)) = sk3.
% 1.49/0.69 Proof:
% 1.49/0.69 join(sk1, join(sk2, sk3))
% 1.49/0.69 = { by axiom 7 (maddux2_join_associativity_2) }
% 1.49/0.69 join(join(sk1, sk2), sk3)
% 1.49/0.69 = { by axiom 8 (goals_14) }
% 1.49/0.69 sk3
% 1.49/0.69
% 1.49/0.69 Lemma 28: join(sk2, join(sk1, sk3)) = sk3.
% 1.49/0.69 Proof:
% 1.49/0.69 join(sk2, join(sk1, sk3))
% 1.49/0.69 = { by lemma 26 }
% 1.49/0.69 join(sk3, join(sk1, sk2))
% 1.49/0.69 = { by lemma 24 R->L }
% 1.49/0.69 join(sk1, join(sk2, sk3))
% 1.49/0.69 = { by lemma 27 }
% 1.49/0.69 sk3
% 1.49/0.69
% 1.49/0.69 Goal 1 (goals_15): tuple(join(sk1, sk3), join(sk2, sk3)) = tuple(sk3, sk3).
% 1.49/0.69 Proof:
% 1.49/0.69 tuple(join(sk1, sk3), join(sk2, sk3))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 1.49/0.69 tuple(join(sk1, sk3), join(sk3, sk2))
% 1.49/0.69 = { by lemma 27 R->L }
% 1.49/0.69 tuple(join(sk1, sk3), join(join(sk1, join(sk2, sk3)), sk2))
% 1.49/0.69 = { by axiom 7 (maddux2_join_associativity_2) R->L }
% 1.49/0.69 tuple(join(sk1, sk3), join(sk1, join(join(sk2, sk3), sk2)))
% 1.49/0.69 = { by axiom 1 (maddux1_join_commutativity_1) }
% 1.49/0.69 tuple(join(sk1, sk3), join(sk1, join(sk2, join(sk2, sk3))))
% 1.49/0.69 = { by lemma 25 }
% 1.49/0.69 tuple(join(sk1, sk3), join(sk1, join(sk2, sk3)))
% 1.49/0.69 = { by lemma 27 }
% 1.49/0.69 tuple(join(sk1, sk3), sk3)
% 1.49/0.69 = { by lemma 23 R->L }
% 1.49/0.69 tuple(join(join(sk1, sk3), join(sk1, sk3)), sk3)
% 1.49/0.69 = { by lemma 26 }
% 1.49/0.69 tuple(join(sk3, join(sk1, join(sk1, sk3))), sk3)
% 1.49/0.69 = { by lemma 25 }
% 1.49/0.69 tuple(join(sk3, join(sk1, sk3)), sk3)
% 1.49/0.69 = { by lemma 28 R->L }
% 1.49/0.69 tuple(join(join(sk2, join(sk1, sk3)), join(sk1, sk3)), sk3)
% 1.49/0.69 = { by axiom 7 (maddux2_join_associativity_2) R->L }
% 1.49/0.69 tuple(join(sk2, join(join(sk1, sk3), join(sk1, sk3))), sk3)
% 1.49/0.69 = { by lemma 23 }
% 1.49/0.69 tuple(join(sk2, join(sk1, sk3)), sk3)
% 1.49/0.69 = { by lemma 28 }
% 1.49/0.69 tuple(sk3, sk3)
% 1.49/0.69 % SZS output end Proof
% 1.49/0.69
% 1.49/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------