%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:33:05 PM UTC 2026
% Result : Unsatisfiable 0.06s 0.40s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 22:50:39 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.06/0.40
% 0.06/0.40 % SZS status Unsatisfiable
% 0.06/0.40
% 0.06/0.41 % SZS output start Proof
% 0.06/0.41 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 0.06/0.41 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.06/0.41 Axiom 3 (def_top_12): top = join(X, complement(X)).
% 0.06/0.41 Axiom 4 (converse_idempotence_8): converse(converse(X)) = X.
% 0.06/0.41 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 0.06/0.41 Axiom 6 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.06/0.41 Axiom 7 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.06/0.41 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.06/0.41 Axiom 9 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.06/0.41 Axiom 10 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.06/0.41 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.06/0.41 Axiom 12 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.06/0.41 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.06/0.41
% 0.06/0.41 Lemma 14: complement(top) = zero.
% 0.06/0.41 Proof:
% 0.06/0.41 complement(top)
% 0.06/0.41 = { by axiom 3 (def_top_12) }
% 0.06/0.41 complement(join(complement(X), complement(complement(X))))
% 0.06/0.41 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 0.06/0.41 meet(X, complement(X))
% 0.06/0.42 = { by axiom 5 (def_zero_13) R->L }
% 0.06/0.42 zero
% 0.06/0.42
% 0.06/0.42 Lemma 15: composition(converse(one), X) = X.
% 0.06/0.42 Proof:
% 0.06/0.42 composition(converse(one), X)
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) R->L }
% 0.06/0.42 composition(converse(one), converse(converse(X)))
% 0.06/0.42 = { by axiom 7 (converse_multiplicativity_10) R->L }
% 0.06/0.42 converse(composition(converse(X), one))
% 0.06/0.42 = { by axiom 1 (composition_identity_6) }
% 0.06/0.42 converse(converse(X))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) }
% 0.06/0.42 X
% 0.06/0.42
% 0.06/0.42 Lemma 16: converse(one) = one.
% 0.06/0.42 Proof:
% 0.06/0.42 converse(one)
% 0.06/0.42 = { by axiom 1 (composition_identity_6) R->L }
% 0.06/0.42 composition(converse(one), one)
% 0.06/0.42 = { by lemma 15 }
% 0.06/0.42 one
% 0.06/0.42
% 0.06/0.42 Lemma 17: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.06/0.42 Proof:
% 0.06/0.42 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.06/0.42 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 0.06/0.42 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.06/0.42 = { by axiom 12 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.06/0.42 X
% 0.06/0.42
% 0.06/0.42 Lemma 18: composition(one, X) = X.
% 0.06/0.42 Proof:
% 0.06/0.42 composition(one, X)
% 0.06/0.42 = { by lemma 15 R->L }
% 0.06/0.42 composition(converse(one), composition(one, X))
% 0.06/0.42 = { by axiom 8 (composition_associativity_5) }
% 0.06/0.42 composition(composition(converse(one), one), X)
% 0.06/0.42 = { by axiom 1 (composition_identity_6) }
% 0.06/0.42 composition(converse(one), X)
% 0.06/0.42 = { by lemma 15 }
% 0.06/0.42 X
% 0.06/0.42
% 0.06/0.42 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 0.06/0.42 Proof:
% 0.06/0.42 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 0.06/0.42 = { by axiom 13 (converse_cancellativity_11) }
% 0.06/0.42 complement(X)
% 0.06/0.42
% 0.06/0.42 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 0.06/0.42 Proof:
% 0.06/0.42 join(complement(X), complement(X))
% 0.06/0.42 = { by lemma 15 R->L }
% 0.06/0.42 join(complement(X), composition(converse(one), complement(X)))
% 0.06/0.42 = { by lemma 18 R->L }
% 0.06/0.42 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.06/0.42 = { by lemma 19 }
% 0.06/0.42 complement(X)
% 0.06/0.42
% 0.06/0.42 Lemma 21: join(zero, zero) = zero.
% 0.06/0.42 Proof:
% 0.06/0.42 join(zero, zero)
% 0.06/0.42 = { by lemma 14 R->L }
% 0.06/0.42 join(zero, complement(top))
% 0.06/0.42 = { by lemma 14 R->L }
% 0.06/0.42 join(complement(top), complement(top))
% 0.06/0.42 = { by lemma 20 }
% 0.06/0.42 complement(top)
% 0.06/0.42 = { by lemma 14 }
% 0.06/0.42 zero
% 0.06/0.42
% 0.06/0.42 Lemma 22: join(zero, join(zero, X)) = join(X, zero).
% 0.06/0.42 Proof:
% 0.06/0.42 join(zero, join(zero, X))
% 0.06/0.42 = { by axiom 10 (maddux2_join_associativity_2) }
% 0.06/0.42 join(join(zero, zero), X)
% 0.06/0.42 = { by lemma 21 }
% 0.06/0.42 join(zero, X)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 join(X, zero)
% 0.06/0.42
% 0.06/0.42 Lemma 23: join(X, zero) = X.
% 0.06/0.42 Proof:
% 0.06/0.42 join(X, zero)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(zero, X)
% 0.06/0.42 = { by lemma 17 R->L }
% 0.06/0.42 join(zero, join(meet(X, complement(X)), complement(join(complement(X), complement(X)))))
% 0.06/0.42 = { by axiom 5 (def_zero_13) R->L }
% 0.06/0.42 join(zero, join(zero, complement(join(complement(X), complement(X)))))
% 0.06/0.42 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 0.06/0.42 join(zero, join(zero, meet(X, X)))
% 0.06/0.42 = { by lemma 22 }
% 0.06/0.42 join(meet(X, X), zero)
% 0.06/0.42 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 0.06/0.42 join(complement(join(complement(X), complement(X))), zero)
% 0.06/0.42 = { by lemma 20 }
% 0.06/0.42 join(complement(complement(X)), zero)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 join(zero, complement(complement(X)))
% 0.06/0.42 = { by axiom 5 (def_zero_13) }
% 0.06/0.42 join(meet(X, complement(X)), complement(complement(X)))
% 0.06/0.42 = { by lemma 20 R->L }
% 0.06/0.42 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.06/0.42 = { by lemma 17 }
% 0.06/0.42 X
% 0.06/0.42
% 0.06/0.42 Lemma 24: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 0.06/0.42 Proof:
% 0.06/0.42 converse(join(X, converse(Y)))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 converse(join(converse(Y), X))
% 0.06/0.42 = { by axiom 9 (converse_additivity_9) }
% 0.06/0.42 join(converse(converse(Y)), converse(X))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) }
% 0.06/0.42 join(Y, converse(X))
% 0.06/0.42
% 0.06/0.42 Lemma 25: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 0.06/0.42 Proof:
% 0.06/0.42 converse(join(converse(X), Y))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 converse(join(Y, converse(X)))
% 0.06/0.42 = { by lemma 24 }
% 0.06/0.42 join(X, converse(Y))
% 0.06/0.42
% 0.06/0.42 Lemma 26: converse(zero) = zero.
% 0.06/0.42 Proof:
% 0.06/0.42 converse(zero)
% 0.06/0.42 = { by lemma 23 R->L }
% 0.06/0.42 join(converse(zero), zero)
% 0.06/0.42 = { by lemma 22 R->L }
% 0.06/0.42 join(zero, join(zero, converse(zero)))
% 0.06/0.42 = { by lemma 25 R->L }
% 0.06/0.42 join(zero, converse(join(converse(zero), zero)))
% 0.06/0.42 = { by lemma 23 }
% 0.06/0.42 join(zero, converse(converse(zero)))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) }
% 0.06/0.42 join(zero, zero)
% 0.06/0.42 = { by lemma 21 }
% 0.06/0.42 zero
% 0.06/0.42
% 0.06/0.42 Lemma 27: join(X, join(Y, complement(X))) = join(Y, top).
% 0.06/0.42 Proof:
% 0.06/0.42 join(X, join(Y, complement(X)))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(X, join(complement(X), Y))
% 0.06/0.42 = { by axiom 10 (maddux2_join_associativity_2) }
% 0.06/0.42 join(join(X, complement(X)), Y)
% 0.06/0.42 = { by axiom 3 (def_top_12) R->L }
% 0.06/0.42 join(top, Y)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 join(Y, top)
% 0.06/0.42
% 0.06/0.42 Lemma 28: join(top, complement(X)) = top.
% 0.06/0.42 Proof:
% 0.06/0.42 join(top, complement(X))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(complement(X), top)
% 0.06/0.42 = { by lemma 27 R->L }
% 0.06/0.42 join(X, join(complement(X), complement(X)))
% 0.06/0.42 = { by lemma 20 }
% 0.06/0.42 join(X, complement(X))
% 0.06/0.42 = { by axiom 3 (def_top_12) R->L }
% 0.06/0.42 top
% 0.06/0.42
% 0.06/0.42 Lemma 29: join(Y, top) = join(X, top).
% 0.06/0.42 Proof:
% 0.06/0.42 join(Y, top)
% 0.06/0.42 = { by lemma 28 R->L }
% 0.06/0.42 join(Y, join(top, complement(Y)))
% 0.06/0.42 = { by lemma 27 }
% 0.06/0.42 join(top, top)
% 0.06/0.42 = { by lemma 27 R->L }
% 0.06/0.42 join(X, join(top, complement(X)))
% 0.06/0.42 = { by lemma 28 }
% 0.06/0.42 join(X, top)
% 0.06/0.42
% 0.06/0.42 Lemma 30: join(zero, X) = X.
% 0.06/0.42 Proof:
% 0.06/0.42 join(zero, X)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(X, zero)
% 0.06/0.42 = { by lemma 23 }
% 0.06/0.42 X
% 0.06/0.42
% 0.06/0.42 Lemma 31: join(X, top) = top.
% 0.06/0.42 Proof:
% 0.06/0.42 join(X, top)
% 0.06/0.42 = { by lemma 29 }
% 0.06/0.42 join(zero, top)
% 0.06/0.42 = { by lemma 30 }
% 0.06/0.42 top
% 0.06/0.42
% 0.06/0.42 Lemma 32: join(top, X) = top.
% 0.06/0.42 Proof:
% 0.06/0.42 join(top, X)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(X, top)
% 0.06/0.42 = { by lemma 29 R->L }
% 0.06/0.42 join(Y, top)
% 0.06/0.42 = { by lemma 31 }
% 0.06/0.42 top
% 0.06/0.42
% 0.06/0.42 Lemma 33: join(X, composition(Y, X)) = composition(join(Y, one), X).
% 0.06/0.42 Proof:
% 0.06/0.42 join(X, composition(Y, X))
% 0.06/0.42 = { by lemma 18 R->L }
% 0.06/0.42 join(composition(one, X), composition(Y, X))
% 0.06/0.42 = { by axiom 11 (composition_distributivity_7) R->L }
% 0.06/0.42 composition(join(one, Y), X)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 composition(join(Y, one), X)
% 0.06/0.42
% 0.06/0.42 Lemma 34: composition(X, join(one, one)) = join(X, X).
% 0.06/0.42 Proof:
% 0.06/0.42 composition(X, join(one, one))
% 0.06/0.42 = { by lemma 16 R->L }
% 0.06/0.42 composition(X, join(one, converse(one)))
% 0.06/0.42 = { by lemma 16 R->L }
% 0.06/0.42 composition(X, join(converse(one), converse(one)))
% 0.06/0.42 = { by axiom 9 (converse_additivity_9) R->L }
% 0.06/0.42 composition(X, converse(join(one, one)))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) R->L }
% 0.06/0.42 composition(converse(converse(X)), converse(join(one, one)))
% 0.06/0.42 = { by axiom 7 (converse_multiplicativity_10) R->L }
% 0.06/0.42 converse(composition(join(one, one), converse(X)))
% 0.06/0.42 = { by lemma 16 R->L }
% 0.06/0.42 converse(composition(join(converse(one), one), converse(X)))
% 0.06/0.42 = { by lemma 33 R->L }
% 0.06/0.42 converse(join(converse(X), composition(converse(one), converse(X))))
% 0.06/0.42 = { by lemma 15 }
% 0.06/0.42 converse(join(converse(X), converse(X)))
% 0.06/0.42 = { by lemma 25 }
% 0.06/0.42 join(X, converse(converse(X)))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) }
% 0.06/0.42 join(X, X)
% 0.06/0.42
% 0.06/0.42 Lemma 35: join(composition(X, zero), composition(X, zero)) = composition(X, zero).
% 0.06/0.42 Proof:
% 0.06/0.42 join(composition(X, zero), composition(X, zero))
% 0.06/0.42 = { by lemma 34 R->L }
% 0.06/0.42 composition(composition(X, zero), join(one, one))
% 0.06/0.42 = { by axiom 8 (composition_associativity_5) R->L }
% 0.06/0.42 composition(X, composition(zero, join(one, one)))
% 0.06/0.42 = { by lemma 34 }
% 0.06/0.42 composition(X, join(zero, zero))
% 0.06/0.42 = { by lemma 21 }
% 0.06/0.42 composition(X, zero)
% 0.06/0.42
% 0.06/0.42 Lemma 36: join(X, converse(top)) = converse(top).
% 0.06/0.42 Proof:
% 0.06/0.42 join(X, converse(top))
% 0.06/0.42 = { by lemma 24 R->L }
% 0.06/0.42 converse(join(top, converse(X)))
% 0.06/0.42 = { by lemma 32 }
% 0.06/0.42 converse(top)
% 0.06/0.42
% 0.06/0.42 Lemma 37: composition(top, zero) = zero.
% 0.06/0.42 Proof:
% 0.06/0.42 composition(top, zero)
% 0.06/0.42 = { by lemma 14 R->L }
% 0.06/0.42 composition(top, complement(top))
% 0.06/0.42 = { by lemma 32 R->L }
% 0.06/0.42 composition(join(top, one), complement(top))
% 0.06/0.42 = { by lemma 31 R->L }
% 0.06/0.42 composition(join(join(converse(top), top), one), complement(top))
% 0.06/0.42 = { by lemma 30 R->L }
% 0.06/0.42 composition(join(join(zero, join(converse(top), top)), one), complement(top))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 composition(join(join(zero, join(top, converse(top))), one), complement(top))
% 0.06/0.42 = { by lemma 36 }
% 0.06/0.42 composition(join(join(zero, converse(top)), one), complement(top))
% 0.06/0.42 = { by lemma 36 }
% 0.06/0.42 composition(join(converse(top), one), complement(top))
% 0.06/0.42 = { by lemma 33 R->L }
% 0.06/0.42 join(complement(top), composition(converse(top), complement(top)))
% 0.06/0.42 = { by lemma 32 R->L }
% 0.06/0.42 join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))
% 0.06/0.42 = { by lemma 33 }
% 0.06/0.42 join(complement(top), composition(converse(top), complement(composition(join(top, one), top))))
% 0.06/0.42 = { by lemma 32 }
% 0.06/0.42 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 0.06/0.42 = { by lemma 19 }
% 0.06/0.42 complement(top)
% 0.06/0.42 = { by lemma 14 }
% 0.06/0.42 zero
% 0.06/0.42
% 0.06/0.42 Lemma 38: composition(X, zero) = zero.
% 0.06/0.42 Proof:
% 0.06/0.42 composition(X, zero)
% 0.06/0.42 = { by lemma 35 R->L }
% 0.06/0.42 join(composition(X, zero), composition(X, zero))
% 0.06/0.42 = { by lemma 30 R->L }
% 0.06/0.42 join(composition(X, zero), join(zero, composition(X, zero)))
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.06/0.42 join(composition(X, zero), join(composition(X, zero), zero))
% 0.06/0.42 = { by axiom 10 (maddux2_join_associativity_2) }
% 0.06/0.42 join(join(composition(X, zero), composition(X, zero)), zero)
% 0.06/0.42 = { by lemma 35 }
% 0.06/0.42 join(composition(X, zero), zero)
% 0.06/0.42 = { by lemma 37 R->L }
% 0.06/0.42 join(composition(X, zero), composition(top, zero))
% 0.06/0.42 = { by axiom 11 (composition_distributivity_7) R->L }
% 0.06/0.42 composition(join(X, top), zero)
% 0.06/0.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.06/0.42 composition(join(top, X), zero)
% 0.06/0.42 = { by lemma 32 }
% 0.06/0.42 composition(top, zero)
% 0.06/0.42 = { by lemma 37 }
% 0.06/0.42 zero
% 0.06/0.42
% 0.06/0.42 Goal 1 (goals_14): tuple(composition(zero, sk1), composition(sk1, zero)) = tuple(zero, zero).
% 0.06/0.42 Proof:
% 0.06/0.42 tuple(composition(zero, sk1), composition(sk1, zero))
% 0.06/0.42 = { by axiom 4 (converse_idempotence_8) R->L }
% 0.06/0.42 tuple(converse(converse(composition(zero, sk1))), composition(sk1, zero))
% 0.06/0.42 = { by axiom 7 (converse_multiplicativity_10) }
% 0.06/0.42 tuple(converse(composition(converse(sk1), converse(zero))), composition(sk1, zero))
% 0.06/0.42 = { by lemma 26 }
% 0.06/0.42 tuple(converse(composition(converse(sk1), zero)), composition(sk1, zero))
% 0.06/0.42 = { by lemma 38 }
% 0.06/0.42 tuple(converse(zero), composition(sk1, zero))
% 0.06/0.42 = { by lemma 26 }
% 0.06/0.42 tuple(zero, composition(sk1, zero))
% 0.06/0.42 = { by lemma 38 }
% 0.06/0.42 tuple(zero, zero)
% 0.06/0.42 % SZS output end Proof
% 0.06/0.42
% 0.06/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------