TSTP Solution File: LAT043-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT043-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n021.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 06:27:15 EDT 2023
% Result : Unsatisfiable 0.15s 0.42s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT043-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Thu Aug 24 05:11:54 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.15/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.15/0.42
% 0.15/0.42 % SZS status Unsatisfiable
% 0.15/0.42
% 0.15/0.44 % SZS output start Proof
% 0.15/0.44 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.15/0.44 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.15/0.44 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 0.15/0.44 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.15/0.44 Axiom 5 (invertability2): meet(complement(X), X) = n0.
% 0.15/0.44 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.15/0.44 Axiom 7 (invertability1): join(complement(X), X) = n1.
% 0.15/0.44 Axiom 8 (invertability3): complement(complement(X)) = X.
% 0.15/0.44 Axiom 9 (distributivity): meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)).
% 0.15/0.44
% 0.15/0.44 Lemma 10: join(X, complement(X)) = n1.
% 0.15/0.44 Proof:
% 0.15/0.44 join(X, complement(X))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 join(complement(X), X)
% 0.15/0.44 = { by axiom 7 (invertability1) }
% 0.15/0.44 n1
% 0.15/0.44
% 0.15/0.44 Lemma 11: meet(X, n1) = X.
% 0.15/0.44 Proof:
% 0.15/0.44 meet(X, n1)
% 0.15/0.44 = { by lemma 10 R->L }
% 0.15/0.44 meet(X, join(X, complement(X)))
% 0.15/0.44 = { by axiom 3 (absorption1) }
% 0.15/0.44 X
% 0.15/0.44
% 0.15/0.44 Lemma 12: meet(X, complement(X)) = n0.
% 0.15/0.44 Proof:
% 0.15/0.44 meet(X, complement(X))
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.15/0.44 meet(complement(X), X)
% 0.15/0.44 = { by axiom 5 (invertability2) }
% 0.15/0.44 n0
% 0.15/0.44
% 0.15/0.44 Lemma 13: join(X, n0) = X.
% 0.15/0.44 Proof:
% 0.15/0.44 join(X, n0)
% 0.15/0.44 = { by lemma 12 R->L }
% 0.15/0.44 join(X, meet(X, complement(X)))
% 0.15/0.44 = { by axiom 6 (absorption2) }
% 0.15/0.44 X
% 0.15/0.44
% 0.15/0.44 Lemma 14: join(n0, X) = X.
% 0.15/0.44 Proof:
% 0.15/0.44 join(n0, X)
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 join(X, n0)
% 0.15/0.44 = { by lemma 13 }
% 0.15/0.44 X
% 0.15/0.44
% 0.15/0.44 Lemma 15: meet(X, join(Y, complement(X))) = meet(Y, X).
% 0.15/0.44 Proof:
% 0.15/0.44 meet(X, join(Y, complement(X)))
% 0.15/0.44 = { by axiom 9 (distributivity) }
% 0.15/0.44 join(meet(X, Y), meet(X, complement(X)))
% 0.15/0.44 = { by lemma 12 }
% 0.15/0.44 join(meet(X, Y), n0)
% 0.15/0.44 = { by lemma 13 }
% 0.15/0.44 meet(X, Y)
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) }
% 0.15/0.44 meet(Y, X)
% 0.15/0.44
% 0.15/0.44 Lemma 16: meet(X, meet(Y, complement(X))) = n0.
% 0.15/0.44 Proof:
% 0.15/0.44 meet(X, meet(Y, complement(X)))
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.15/0.44 meet(meet(Y, complement(X)), X)
% 0.15/0.44 = { by lemma 15 R->L }
% 0.15/0.44 meet(X, join(meet(Y, complement(X)), complement(X)))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 meet(X, join(complement(X), meet(Y, complement(X))))
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.15/0.44 meet(X, join(complement(X), meet(complement(X), Y)))
% 0.15/0.44 = { by axiom 6 (absorption2) }
% 0.15/0.44 meet(X, complement(X))
% 0.15/0.44 = { by lemma 12 }
% 0.15/0.44 n0
% 0.15/0.44
% 0.15/0.44 Lemma 17: meet(complement(X), join(Y, meet(Z, X))) = meet(Y, complement(X)).
% 0.15/0.44 Proof:
% 0.15/0.44 meet(complement(X), join(Y, meet(Z, X)))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 meet(complement(X), join(meet(Z, X), Y))
% 0.15/0.44 = { by axiom 9 (distributivity) }
% 0.15/0.44 join(meet(complement(X), meet(Z, X)), meet(complement(X), Y))
% 0.15/0.44 = { by axiom 4 (associativity_of_meet) R->L }
% 0.15/0.44 join(meet(meet(complement(X), Z), X), meet(complement(X), Y))
% 0.15/0.44 = { by lemma 15 R->L }
% 0.15/0.44 join(meet(X, join(meet(complement(X), Z), complement(X))), meet(complement(X), Y))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) }
% 0.15/0.44 join(meet(X, join(complement(X), meet(complement(X), Z))), meet(complement(X), Y))
% 0.15/0.44 = { by axiom 6 (absorption2) }
% 0.15/0.44 join(meet(X, complement(X)), meet(complement(X), Y))
% 0.15/0.44 = { by lemma 12 }
% 0.15/0.44 join(n0, meet(complement(X), Y))
% 0.15/0.44 = { by lemma 14 }
% 0.15/0.44 meet(complement(X), Y)
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) }
% 0.15/0.44 meet(Y, complement(X))
% 0.15/0.44
% 0.15/0.44 Goal 1 (prove_compatability_law): complement(join(c, d)) = meet(complement(c), complement(d)).
% 0.15/0.44 Proof:
% 0.15/0.44 complement(join(c, d))
% 0.15/0.44 = { by lemma 11 R->L }
% 0.15/0.44 meet(complement(join(c, d)), n1)
% 0.15/0.44 = { by lemma 10 R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(c, complement(c)))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(complement(c), c))
% 0.15/0.44 = { by axiom 3 (absorption1) R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(complement(c), meet(c, join(c, d))))
% 0.15/0.44 = { by lemma 17 }
% 0.15/0.44 meet(complement(c), complement(join(c, d)))
% 0.15/0.44 = { by axiom 1 (commutativity_of_meet) }
% 0.15/0.44 meet(complement(join(c, d)), complement(c))
% 0.15/0.44 = { by lemma 11 R->L }
% 0.15/0.44 meet(complement(join(c, d)), meet(complement(c), n1))
% 0.15/0.44 = { by lemma 10 R->L }
% 0.15/0.44 meet(complement(join(c, d)), meet(complement(c), join(d, complement(d))))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) R->L }
% 0.15/0.44 meet(complement(join(c, d)), meet(complement(c), join(complement(d), d)))
% 0.15/0.44 = { by axiom 9 (distributivity) }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), meet(complement(c), d)))
% 0.15/0.44 = { by lemma 14 R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), join(n0, meet(complement(c), d))))
% 0.15/0.44 = { by lemma 12 R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), join(meet(complement(c), complement(complement(c))), meet(complement(c), d))))
% 0.15/0.44 = { by axiom 9 (distributivity) R->L }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), meet(complement(c), join(complement(complement(c)), d))))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), meet(complement(c), join(d, complement(complement(c))))))
% 0.15/0.44 = { by axiom 8 (invertability3) }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), meet(complement(c), join(d, c))))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) }
% 0.15/0.44 meet(complement(join(c, d)), join(meet(complement(c), complement(d)), meet(complement(c), join(c, d))))
% 0.15/0.44 = { by lemma 17 }
% 0.15/0.44 meet(meet(complement(c), complement(d)), complement(join(c, d)))
% 0.15/0.44 = { by lemma 14 R->L }
% 0.15/0.44 join(n0, meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 12 R->L }
% 0.15/0.44 join(meet(c, complement(c)), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 6 (absorption2) R->L }
% 0.15/0.44 join(meet(c, join(complement(c), meet(complement(c), complement(d)))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) }
% 0.15/0.44 join(meet(c, join(meet(complement(c), complement(d)), complement(c))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 15 }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), c), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 14 R->L }
% 0.15/0.44 join(join(n0, meet(meet(complement(c), complement(d)), c)), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 16 R->L }
% 0.15/0.44 join(join(meet(meet(complement(c), complement(d)), meet(d, complement(meet(complement(c), complement(d))))), meet(meet(complement(c), complement(d)), c)), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 9 (distributivity) R->L }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(meet(d, complement(meet(complement(c), complement(d)))), c)), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 2 (commutativity_of_join) }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, meet(d, complement(meet(complement(c), complement(d)))))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 14 R->L }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, join(n0, meet(d, complement(meet(complement(c), complement(d))))))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 16 R->L }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, join(meet(d, meet(complement(c), complement(d))), meet(d, complement(meet(complement(c), complement(d))))))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 9 (distributivity) R->L }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, meet(d, join(meet(complement(c), complement(d)), complement(meet(complement(c), complement(d))))))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 10 }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, meet(d, n1))), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by lemma 11 }
% 0.15/0.44 join(meet(meet(complement(c), complement(d)), join(c, d)), meet(meet(complement(c), complement(d)), complement(join(c, d))))
% 0.15/0.44 = { by axiom 9 (distributivity) R->L }
% 0.15/0.44 meet(meet(complement(c), complement(d)), join(join(c, d), complement(join(c, d))))
% 0.15/0.44 = { by lemma 10 }
% 0.15/0.44 meet(meet(complement(c), complement(d)), n1)
% 0.15/0.44 = { by lemma 11 }
% 0.15/0.44 meet(complement(c), complement(d))
% 0.15/0.44 % SZS output end Proof
% 0.15/0.44
% 0.15/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------