TSTP Solution File: REL023-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL023-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:44:03 EDT 2023
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL023-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 21:25:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Command-line arguments: --no-flatten-goal
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 0.19/0.47 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 0.19/0.47 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.19/0.47 Axiom 4 (def_zero_13): zero = meet(X, complement(X)).
% 0.19/0.47 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 0.19/0.47 Axiom 6 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.19/0.47 Axiom 7 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.19/0.47 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.19/0.47 Axiom 9 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.19/0.48 Axiom 10 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.19/0.48 Axiom 11 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.19/0.48 Axiom 12 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.19/0.48
% 0.19/0.48 Lemma 13: complement(top) = zero.
% 0.19/0.48 Proof:
% 0.19/0.48 complement(top)
% 0.19/0.48 = { by axiom 5 (def_top_12) }
% 0.19/0.48 complement(join(complement(X), complement(complement(X))))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 meet(X, complement(X))
% 0.19/0.48 = { by axiom 4 (def_zero_13) R->L }
% 0.19/0.48 zero
% 0.19/0.48
% 0.19/0.48 Lemma 14: join(X, join(Y, complement(X))) = join(Y, top).
% 0.19/0.48 Proof:
% 0.19/0.48 join(X, join(Y, complement(X)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 join(X, join(complement(X), Y))
% 0.19/0.48 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.19/0.48 join(join(X, complement(X)), Y)
% 0.19/0.48 = { by axiom 5 (def_top_12) R->L }
% 0.19/0.48 join(top, Y)
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) }
% 0.19/0.48 join(Y, top)
% 0.19/0.48
% 0.19/0.48 Lemma 15: composition(converse(one), X) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 composition(converse(one), X)
% 0.19/0.48 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.19/0.48 composition(converse(one), converse(converse(X)))
% 0.19/0.48 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 0.19/0.48 converse(composition(converse(X), one))
% 0.19/0.48 = { by axiom 2 (composition_identity_6) }
% 0.19/0.48 converse(converse(X))
% 0.19/0.48 = { by axiom 1 (converse_idempotence_8) }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 16: join(complement(X), complement(X)) = complement(X).
% 0.19/0.48 Proof:
% 0.19/0.48 join(complement(X), complement(X))
% 0.19/0.48 = { by lemma 15 R->L }
% 0.19/0.48 join(complement(X), composition(converse(one), complement(X)))
% 0.19/0.48 = { by lemma 15 R->L }
% 0.19/0.48 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.19/0.48 = { by axiom 2 (composition_identity_6) R->L }
% 0.19/0.48 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.19/0.48 = { by axiom 7 (composition_associativity_5) R->L }
% 0.19/0.48 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.19/0.48 = { by lemma 15 }
% 0.19/0.48 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.19/0.48 = { by axiom 11 (converse_cancellativity_11) }
% 0.19/0.48 complement(X)
% 0.19/0.48
% 0.19/0.48 Lemma 17: join(top, complement(X)) = top.
% 0.19/0.48 Proof:
% 0.19/0.48 join(top, complement(X))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 join(complement(X), top)
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 join(X, join(complement(X), complement(X)))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 join(X, complement(X))
% 0.19/0.48 = { by axiom 5 (def_top_12) R->L }
% 0.19/0.48 top
% 0.19/0.48
% 0.19/0.48 Lemma 18: join(X, top) = top.
% 0.19/0.48 Proof:
% 0.19/0.48 join(X, top)
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 join(X, join(top, complement(X)))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 join(top, top)
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 join(join(zero, zero), join(top, complement(join(zero, zero))))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 join(join(zero, zero), top)
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 join(top, join(zero, zero))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 join(top, join(zero, complement(top)))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 join(top, join(complement(top), complement(top)))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 join(top, complement(top))
% 0.19/0.48 = { by axiom 5 (def_top_12) R->L }
% 0.19/0.48 top
% 0.19/0.48
% 0.19/0.48 Lemma 19: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.19/0.48 = { by axiom 12 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 20: join(zero, meet(X, X)) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 join(zero, meet(X, X))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 join(zero, complement(join(complement(X), complement(X))))
% 0.19/0.48 = { by axiom 4 (def_zero_13) }
% 0.19/0.48 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.19/0.48 = { by lemma 19 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 21: complement(complement(X)) = meet(X, X).
% 0.19/0.48 Proof:
% 0.19/0.48 complement(complement(X))
% 0.19/0.48 = { by lemma 16 R->L }
% 0.19/0.48 complement(join(complement(X), complement(X)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 meet(X, X)
% 0.19/0.48
% 0.19/0.48 Lemma 22: meet(Y, X) = meet(X, Y).
% 0.19/0.48 Proof:
% 0.19/0.48 meet(Y, X)
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 complement(join(complement(Y), complement(X)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 complement(join(complement(X), complement(Y)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 meet(X, Y)
% 0.19/0.48
% 0.19/0.48 Lemma 23: complement(join(zero, complement(X))) = meet(X, top).
% 0.19/0.48 Proof:
% 0.19/0.48 complement(join(zero, complement(X)))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 complement(join(complement(top), complement(X)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 meet(top, X)
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 meet(X, top)
% 0.19/0.48
% 0.19/0.48 Lemma 24: join(X, complement(zero)) = top.
% 0.19/0.48 Proof:
% 0.19/0.48 join(X, complement(zero))
% 0.19/0.48 = { by lemma 20 R->L }
% 0.19/0.48 join(join(zero, meet(X, X)), complement(zero))
% 0.19/0.48 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 0.19/0.48 join(zero, join(meet(X, X), complement(zero)))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 join(meet(X, X), top)
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 top
% 0.19/0.48
% 0.19/0.48 Lemma 25: join(zero, meet(X, top)) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 join(zero, meet(X, top))
% 0.19/0.48 = { by lemma 24 R->L }
% 0.19/0.48 join(zero, meet(X, join(complement(zero), complement(zero))))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 join(zero, meet(X, complement(zero)))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 join(complement(top), meet(X, complement(zero)))
% 0.19/0.48 = { by lemma 24 R->L }
% 0.19/0.48 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 join(meet(X, zero), meet(X, complement(zero)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 join(meet(X, complement(zero)), meet(X, zero))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 0.19/0.48 = { by lemma 19 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 26: join(zero, complement(X)) = complement(X).
% 0.19/0.48 Proof:
% 0.19/0.48 join(zero, complement(X))
% 0.19/0.48 = { by lemma 20 R->L }
% 0.19/0.48 join(zero, complement(join(zero, meet(X, X))))
% 0.19/0.48 = { by lemma 21 R->L }
% 0.19/0.48 join(zero, complement(join(zero, complement(complement(X)))))
% 0.19/0.48 = { by lemma 23 }
% 0.19/0.48 join(zero, meet(complement(X), top))
% 0.19/0.48 = { by lemma 25 }
% 0.19/0.48 complement(X)
% 0.19/0.48
% 0.19/0.48 Lemma 27: complement(complement(X)) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 complement(complement(X))
% 0.19/0.48 = { by lemma 26 R->L }
% 0.19/0.48 join(zero, complement(complement(X)))
% 0.19/0.48 = { by lemma 21 }
% 0.19/0.48 join(zero, meet(X, X))
% 0.19/0.48 = { by lemma 20 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 28: meet(X, top) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 meet(X, top)
% 0.19/0.48 = { by lemma 23 R->L }
% 0.19/0.48 complement(join(zero, complement(X)))
% 0.19/0.48 = { by lemma 26 R->L }
% 0.19/0.48 join(zero, complement(join(zero, complement(X))))
% 0.19/0.48 = { by lemma 23 }
% 0.19/0.48 join(zero, meet(X, top))
% 0.19/0.48 = { by lemma 25 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 29: complement(join(complement(X), meet(Y, Z))) = meet(X, join(complement(Y), complement(Z))).
% 0.19/0.48 Proof:
% 0.19/0.48 complement(join(complement(X), meet(Y, Z)))
% 0.19/0.48 = { by lemma 22 }
% 0.19/0.48 complement(join(complement(X), meet(Z, Y)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.19/0.48 complement(join(meet(Z, Y), complement(X)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 meet(join(complement(Z), complement(Y)), X)
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 meet(X, join(complement(Z), complement(Y)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) }
% 0.19/0.48 meet(X, join(complement(Y), complement(Z)))
% 0.19/0.48
% 0.19/0.48 Lemma 30: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 0.19/0.48 Proof:
% 0.19/0.48 join(complement(X), complement(Y))
% 0.19/0.48 = { by lemma 28 R->L }
% 0.19/0.48 meet(join(complement(X), complement(Y)), top)
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 meet(top, join(complement(X), complement(Y)))
% 0.19/0.48 = { by lemma 29 R->L }
% 0.19/0.48 complement(join(complement(top), meet(X, Y)))
% 0.19/0.48 = { by lemma 13 }
% 0.19/0.48 complement(join(zero, meet(X, Y)))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 complement(join(zero, meet(Y, X)))
% 0.19/0.48 = { by lemma 27 R->L }
% 0.19/0.48 complement(join(zero, complement(complement(meet(Y, X)))))
% 0.19/0.48 = { by lemma 21 }
% 0.19/0.48 complement(join(zero, meet(meet(Y, X), meet(Y, X))))
% 0.19/0.48 = { by lemma 20 }
% 0.19/0.48 complement(meet(Y, X))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 complement(meet(X, Y))
% 0.19/0.48
% 0.19/0.48 Lemma 31: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.19/0.48 Proof:
% 0.19/0.48 complement(meet(X, complement(Y)))
% 0.19/0.48 = { by lemma 22 }
% 0.19/0.48 complement(meet(complement(Y), X))
% 0.19/0.48 = { by lemma 26 R->L }
% 0.19/0.48 complement(meet(join(zero, complement(Y)), X))
% 0.19/0.48 = { by lemma 30 R->L }
% 0.19/0.48 join(complement(join(zero, complement(Y))), complement(X))
% 0.19/0.48 = { by lemma 23 }
% 0.19/0.48 join(meet(Y, top), complement(X))
% 0.19/0.48 = { by lemma 28 }
% 0.19/0.48 join(Y, complement(X))
% 0.19/0.48
% 0.19/0.48 Goal 1 (goals_14): join(composition(meet(sk1, converse(sk2)), meet(sk2, sk3)), composition(sk1, meet(sk2, sk3))) = composition(sk1, meet(sk2, sk3)).
% 0.19/0.48 Proof:
% 0.19/0.48 join(composition(meet(sk1, converse(sk2)), meet(sk2, sk3)), composition(sk1, meet(sk2, sk3)))
% 0.19/0.48 = { by axiom 3 (maddux1_join_commutativity_1) }
% 0.19/0.48 join(composition(sk1, meet(sk2, sk3)), composition(meet(sk1, converse(sk2)), meet(sk2, sk3)))
% 0.19/0.48 = { by axiom 10 (composition_distributivity_7) R->L }
% 0.19/0.48 composition(join(sk1, meet(sk1, converse(sk2))), meet(sk2, sk3))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 composition(join(sk1, meet(sk1, converse(sk2))), meet(sk3, sk2))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.19/0.48 composition(join(sk1, complement(join(complement(sk1), complement(converse(sk2))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 31 R->L }
% 0.19/0.48 composition(complement(meet(join(complement(sk1), complement(converse(sk2))), complement(sk1))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 composition(complement(meet(complement(sk1), join(complement(sk1), complement(converse(sk2))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 31 R->L }
% 0.19/0.48 composition(complement(meet(complement(sk1), complement(meet(converse(sk2), complement(complement(sk1)))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 30 R->L }
% 0.19/0.48 composition(complement(meet(complement(sk1), join(complement(converse(sk2)), complement(complement(complement(sk1)))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 29 R->L }
% 0.19/0.48 composition(complement(complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1)))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 26 R->L }
% 0.19/0.48 composition(complement(join(zero, complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 composition(complement(join(complement(top), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 composition(complement(join(complement(join(complement(converse(sk2)), top)), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 composition(complement(join(complement(join(complement(complement(sk1)), join(complement(converse(sk2)), complement(complement(complement(sk1)))))), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 30 }
% 0.19/0.48 composition(complement(join(complement(join(complement(complement(sk1)), complement(meet(converse(sk2), complement(complement(sk1)))))), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 composition(complement(join(complement(join(complement(complement(sk1)), complement(meet(complement(complement(sk1)), converse(sk2))))), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.19/0.48 composition(complement(join(meet(complement(sk1), meet(complement(complement(sk1)), converse(sk2))), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 22 R->L }
% 0.19/0.48 composition(complement(join(meet(complement(sk1), meet(converse(sk2), complement(complement(sk1)))), complement(join(complement(complement(sk1)), meet(converse(sk2), complement(complement(sk1))))))), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 19 }
% 0.19/0.48 composition(complement(complement(sk1)), meet(sk3, sk2))
% 0.19/0.48 = { by lemma 27 }
% 0.19/0.48 composition(sk1, meet(sk3, sk2))
% 0.19/0.48 = { by lemma 22 }
% 0.19/0.48 composition(sk1, meet(sk2, sk3))
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48
% 0.19/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------