TSTP Solution File: REL002-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL002-1 : 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 : n010.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 13:43:42 EDT 2023
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL002-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 20:07:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.39 Command-line arguments: --flatten
% 0.18/0.39
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 0.18/0.40 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 0.18/0.40 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.18/0.40 Axiom 4 (def_zero_13): zero = meet(X, complement(X)).
% 0.18/0.40 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 0.18/0.40 Axiom 6 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.18/0.40 Axiom 7 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.18/0.40 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.18/0.40 Axiom 9 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.18/0.40 Axiom 10 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.18/0.40
% 0.18/0.40 Lemma 11: join(X, join(Y, complement(X))) = join(Y, top).
% 0.18/0.40 Proof:
% 0.18/0.40 join(X, join(Y, complement(X)))
% 0.18/0.40 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.18/0.40 join(X, join(complement(X), Y))
% 0.18/0.40 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.18/0.40 join(join(X, complement(X)), Y)
% 0.18/0.40 = { by axiom 5 (def_top_12) R->L }
% 0.18/0.40 join(top, Y)
% 0.18/0.40 = { by axiom 3 (maddux1_join_commutativity_1) }
% 0.18/0.40 join(Y, top)
% 0.18/0.40
% 0.18/0.40 Lemma 12: composition(converse(one), X) = X.
% 0.18/0.40 Proof:
% 0.18/0.40 composition(converse(one), X)
% 0.18/0.40 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.18/0.40 composition(converse(one), converse(converse(X)))
% 0.18/0.40 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 0.18/0.40 converse(composition(converse(X), one))
% 0.18/0.40 = { by axiom 2 (composition_identity_6) }
% 0.18/0.40 converse(converse(X))
% 0.18/0.40 = { by axiom 1 (converse_idempotence_8) }
% 0.18/0.40 X
% 0.18/0.40
% 0.18/0.40 Lemma 13: join(top, complement(X)) = top.
% 0.18/0.40 Proof:
% 0.18/0.40 join(top, complement(X))
% 0.18/0.40 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.18/0.40 join(complement(X), top)
% 0.18/0.40 = { by lemma 11 R->L }
% 0.18/0.40 join(X, join(complement(X), complement(X)))
% 0.18/0.40 = { by lemma 12 R->L }
% 0.18/0.40 join(X, join(complement(X), composition(converse(one), complement(X))))
% 0.18/0.40 = { by lemma 12 R->L }
% 0.18/0.40 join(X, join(complement(X), composition(converse(one), complement(composition(converse(one), X)))))
% 0.18/0.40 = { by axiom 2 (composition_identity_6) R->L }
% 0.18/0.40 join(X, join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X)))))
% 0.18/0.40 = { by axiom 7 (composition_associativity_5) R->L }
% 0.18/0.40 join(X, join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X))))))
% 0.18/0.40 = { by lemma 12 }
% 0.18/0.40 join(X, join(complement(X), composition(converse(one), complement(composition(one, X)))))
% 0.18/0.40 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.18/0.40 join(X, join(composition(converse(one), complement(composition(one, X))), complement(X)))
% 0.18/0.40 = { by axiom 10 (converse_cancellativity_11) }
% 0.18/0.40 join(X, complement(X))
% 0.18/0.40 = { by axiom 5 (def_top_12) R->L }
% 0.18/0.40 top
% 0.18/0.40
% 0.18/0.40 Goal 1 (goals_14): join(sk1, top) = top.
% 0.18/0.40 Proof:
% 0.18/0.40 join(sk1, top)
% 0.18/0.40 = { by lemma 13 R->L }
% 0.18/0.40 join(sk1, join(top, complement(sk1)))
% 0.18/0.40 = { by lemma 11 }
% 0.18/0.40 join(top, top)
% 0.18/0.40 = { by lemma 11 R->L }
% 0.18/0.40 join(zero, join(top, complement(zero)))
% 0.18/0.40 = { by lemma 13 }
% 0.18/0.40 join(zero, top)
% 0.18/0.40 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 0.18/0.40 join(top, zero)
% 0.18/0.40 = { by axiom 4 (def_zero_13) }
% 0.18/0.40 join(top, meet(X, complement(X)))
% 0.18/0.40 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.18/0.40 join(top, complement(join(complement(X), complement(complement(X)))))
% 0.18/0.40 = { by axiom 5 (def_top_12) R->L }
% 0.18/0.40 join(top, complement(top))
% 0.18/0.40 = { by axiom 5 (def_top_12) R->L }
% 0.18/0.40 top
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40
% 0.18/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------