%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 11:42:52 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.65s
% Output : Proof 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n005.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 13:57:01 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.65 Command-line arguments: --no-flatten-goal
% 0.30/0.65
% 0.30/0.65 % SZS status Unsatisfiable
% 0.30/0.65
% 0.30/0.67 % SZS output start Proof
% 0.30/0.67 Axiom 1 (wal_absorbtion_2): join(meet(X, X), meet(Y, join(X, X))) = X.
% 0.30/0.67 Axiom 2 (wal_absorbtion_1): join(meet(X, Y), meet(X, join(X, Y))) = X.
% 0.30/0.67 Axiom 3 (wal_absorbtion_3): join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 0.30/0.67 Axiom 4 (wal_absorbtion_5): join(join(meet(X, Y), meet(Z, X)), X) = X.
% 0.30/0.67 Axiom 5 (wal_absorbtion_4): meet(meet(join(X, Y), join(Z, X)), X) = X.
% 0.30/0.67
% 0.30/0.67 Lemma 6: meet(meet(join(X, Y), X), X) = X.
% 0.30/0.67 Proof:
% 0.30/0.67 meet(meet(join(X, Y), X), X)
% 0.30/0.67 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.30/0.67 meet(meet(join(X, Y), join(join(meet(X, Z), meet(W, X)), X)), X)
% 0.30/0.67 = { by axiom 5 (wal_absorbtion_4) }
% 0.30/0.67 X
% 0.30/0.67
% 0.30/0.67 Lemma 7: meet(X, X) = X.
% 0.30/0.67 Proof:
% 0.30/0.67 meet(X, X)
% 0.30/0.67 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.30/0.67 meet(meet(meet(join(X, Y), join(Z, X)), X), X)
% 0.30/0.67 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.30/0.67 meet(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), X))
% 0.30/0.67 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.30/0.67 meet(meet(meet(join(X, Y), join(Z, X)), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.30/0.67 = { by axiom 2 (wal_absorbtion_1) R->L }
% 0.30/0.67 meet(meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), join(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.30/0.68 = { by lemma 6 }
% 0.30/0.68 meet(meet(join(X, Y), join(Z, X)), X)
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) }
% 0.30/0.68 X
% 0.30/0.68
% 0.30/0.68 Lemma 8: join(join(meet(X, Y), X), X) = X.
% 0.30/0.68 Proof:
% 0.30/0.68 join(join(meet(X, Y), X), X)
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.30/0.68 join(join(meet(X, Y), meet(meet(join(X, Z), join(W, X)), X)), X)
% 0.30/0.68 = { by axiom 4 (wal_absorbtion_5) }
% 0.30/0.68 X
% 0.30/0.68
% 0.30/0.68 Lemma 9: join(X, X) = X.
% 0.30/0.68 Proof:
% 0.30/0.68 join(X, X)
% 0.30/0.68 = { by lemma 7 R->L }
% 0.30/0.68 join(X, meet(X, X))
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.30/0.68 join(meet(meet(join(X, X), join(X, X)), X), meet(X, X))
% 0.30/0.68 = { by lemma 7 }
% 0.30/0.68 join(meet(join(X, X), X), meet(X, X))
% 0.30/0.68 = { by lemma 8 R->L }
% 0.30/0.68 join(meet(join(X, X), X), meet(X, join(join(meet(X, X), X), X)))
% 0.30/0.68 = { by lemma 7 }
% 0.30/0.68 join(meet(join(X, X), X), meet(X, join(join(X, X), X)))
% 0.30/0.68 = { by axiom 3 (wal_absorbtion_3) }
% 0.30/0.68 X
% 0.30/0.68
% 0.30/0.68 Lemma 10: join(X, meet(Y, X)) = X.
% 0.30/0.68 Proof:
% 0.30/0.68 join(X, meet(Y, X))
% 0.30/0.68 = { by lemma 7 R->L }
% 0.30/0.68 join(meet(X, X), meet(Y, X))
% 0.30/0.68 = { by lemma 9 R->L }
% 0.30/0.68 join(meet(X, X), meet(Y, join(X, X)))
% 0.30/0.68 = { by axiom 1 (wal_absorbtion_2) }
% 0.30/0.68 X
% 0.30/0.68
% 0.30/0.68 Lemma 11: meet(meet(X, join(Y, X)), X) = X.
% 0.30/0.68 Proof:
% 0.30/0.68 meet(meet(X, join(Y, X)), X)
% 0.30/0.68 = { by axiom 1 (wal_absorbtion_2) R->L }
% 0.30/0.68 meet(meet(join(meet(X, X), meet(meet(join(join(X, X), Z), join(W, join(X, X))), join(X, X))), join(Y, X)), X)
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) }
% 0.30/0.68 meet(meet(join(meet(X, X), join(X, X)), join(Y, X)), X)
% 0.30/0.68 = { by lemma 7 }
% 0.30/0.68 meet(meet(join(X, join(X, X)), join(Y, X)), X)
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) }
% 0.30/0.68 X
% 0.30/0.68
% 0.30/0.68 Lemma 12: meet(meet(X, meet(Y, X)), meet(Y, X)) = meet(Y, X).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(meet(X, meet(Y, X)), meet(Y, X))
% 0.30/0.68 = { by axiom 3 (wal_absorbtion_3) R->L }
% 0.30/0.68 meet(meet(join(meet(Y, X), meet(X, join(Y, X))), meet(Y, X)), meet(Y, X))
% 0.30/0.68 = { by lemma 6 }
% 0.30/0.68 meet(Y, X)
% 0.30/0.68
% 0.30/0.68 Lemma 13: meet(X, meet(Y, X)) = meet(Y, X).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(X, meet(Y, X))
% 0.30/0.68 = { by lemma 8 R->L }
% 0.30/0.68 join(join(meet(meet(X, meet(Y, X)), meet(Y, X)), meet(X, meet(Y, X))), meet(X, meet(Y, X)))
% 0.30/0.68 = { by lemma 12 }
% 0.30/0.68 join(join(meet(Y, X), meet(X, meet(Y, X))), meet(X, meet(Y, X)))
% 0.30/0.68 = { by lemma 10 }
% 0.30/0.68 join(meet(Y, X), meet(X, meet(Y, X)))
% 0.30/0.68 = { by lemma 10 }
% 0.30/0.68 meet(Y, X)
% 0.30/0.68
% 0.30/0.68 Lemma 14: meet(meet(X, Y), Y) = meet(X, Y).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(meet(X, Y), Y)
% 0.30/0.68 = { by lemma 9 R->L }
% 0.30/0.68 join(meet(meet(X, Y), Y), meet(meet(X, Y), Y))
% 0.30/0.68 = { by axiom 2 (wal_absorbtion_1) R->L }
% 0.30/0.68 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(Y, meet(X, Y)), meet(Y, join(Y, meet(X, Y))))))
% 0.30/0.68 = { by lemma 13 }
% 0.30/0.68 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(Y, meet(X, Y))))))
% 0.30/0.68 = { by lemma 10 }
% 0.30/0.68 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, Y))))
% 0.30/0.68 = { by lemma 7 }
% 0.30/0.68 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y)))
% 0.30/0.68 = { by axiom 2 (wal_absorbtion_1) }
% 0.30/0.68 meet(X, Y)
% 0.30/0.68
% 0.30/0.68 Lemma 15: meet(join(meet(X, Y), X), X) = join(meet(X, Y), X).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(join(meet(X, Y), X), X)
% 0.30/0.68 = { by lemma 9 R->L }
% 0.30/0.68 join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), X))
% 0.30/0.68 = { by lemma 8 R->L }
% 0.30/0.68 join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
% 0.30/0.68 = { by axiom 2 (wal_absorbtion_1) }
% 0.30/0.68 join(meet(X, Y), X)
% 0.30/0.68
% 0.30/0.68 Lemma 16: meet(meet(X, Y), X) = meet(X, Y).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(meet(X, Y), X)
% 0.30/0.68 = { by lemma 9 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), X))
% 0.30/0.68 = { by lemma 10 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(X, meet(join(meet(X, Y), X), X))))
% 0.30/0.68 = { by lemma 8 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(X, meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 11 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(meet(X, join(meet(X, Y), X)), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 14 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(meet(meet(X, join(meet(X, Y), X)), join(meet(X, Y), X)), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 15 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(meet(meet(X, join(meet(X, Y), X)), meet(join(meet(X, Y), X), X)), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 15 R->L }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(meet(meet(X, meet(join(meet(X, Y), X), X)), meet(join(meet(X, Y), X), X)), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 12 }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(meet(join(meet(X, Y), X), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by lemma 15 }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))))
% 0.30/0.68 = { by axiom 2 (wal_absorbtion_1) }
% 0.30/0.68 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(X, Y), X)))
% 0.30/0.68 = { by axiom 2 (wal_absorbtion_1) }
% 0.30/0.68 meet(X, Y)
% 0.30/0.68
% 0.30/0.68 Lemma 17: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(meet(X, Y), meet(Y, X))
% 0.30/0.68 = { by axiom 1 (wal_absorbtion_2) R->L }
% 0.30/0.68 meet(meet(X, join(meet(Y, Y), meet(meet(join(Y, Y), X), join(Y, Y)))), meet(Y, X))
% 0.30/0.68 = { by lemma 16 }
% 0.30/0.68 meet(meet(X, join(meet(Y, Y), meet(join(Y, Y), X))), meet(Y, X))
% 0.30/0.68 = { by lemma 7 }
% 0.30/0.68 meet(meet(X, join(Y, meet(join(Y, Y), X))), meet(Y, X))
% 0.30/0.68 = { by lemma 9 }
% 0.30/0.68 meet(meet(X, join(Y, meet(Y, X))), meet(Y, X))
% 0.30/0.68 = { by axiom 3 (wal_absorbtion_3) R->L }
% 0.30/0.68 meet(meet(join(meet(Y, X), meet(X, join(Y, X))), join(Y, meet(Y, X))), meet(Y, X))
% 0.30/0.68 = { by axiom 5 (wal_absorbtion_4) }
% 0.30/0.68 meet(Y, X)
% 0.30/0.68
% 0.30/0.68 Lemma 18: meet(X, Y) = meet(Y, X).
% 0.30/0.68 Proof:
% 0.30/0.68 meet(X, Y)
% 0.30/0.68 = { by lemma 17 R->L }
% 0.30/0.68 meet(meet(Y, X), meet(X, Y))
% 0.30/0.68 = { by lemma 16 R->L }
% 0.30/0.69 meet(meet(meet(Y, X), meet(X, Y)), meet(Y, X))
% 0.30/0.69 = { by lemma 17 }
% 0.30/0.69 meet(meet(X, Y), meet(Y, X))
% 0.30/0.69 = { by lemma 17 }
% 0.30/0.69 meet(Y, X)
% 0.30/0.69
% 0.30/0.69 Lemma 19: meet(X, join(Y, X)) = X.
% 0.30/0.69 Proof:
% 0.30/0.69 meet(X, join(Y, X))
% 0.30/0.69 = { by lemma 16 R->L }
% 0.30/0.69 meet(meet(X, join(Y, X)), X)
% 0.30/0.69 = { by lemma 11 }
% 0.30/0.69 X
% 0.30/0.69
% 0.30/0.69 Lemma 20: meet(join(X, Y), X) = X.
% 0.30/0.69 Proof:
% 0.30/0.69 meet(join(X, Y), X)
% 0.30/0.69 = { by lemma 14 R->L }
% 0.30/0.69 meet(meet(join(X, Y), X), X)
% 0.30/0.69 = { by lemma 6 }
% 0.30/0.69 X
% 0.30/0.69
% 0.30/0.69 Lemma 21: meet(join(X, Y), join(Y, X)) = join(X, Y).
% 0.30/0.69 Proof:
% 0.30/0.69 meet(join(X, Y), join(Y, X))
% 0.30/0.69 = { by lemma 18 R->L }
% 0.30/0.69 meet(join(Y, X), join(X, Y))
% 0.30/0.69 = { by lemma 19 R->L }
% 0.30/0.69 meet(join(Y, X), join(meet(X, join(Y, X)), Y))
% 0.30/0.69 = { by lemma 18 R->L }
% 0.30/0.69 meet(join(Y, X), join(meet(join(Y, X), X), Y))
% 0.30/0.69 = { by lemma 20 R->L }
% 0.30/0.69 meet(join(Y, X), join(meet(join(Y, X), X), meet(join(Y, X), Y)))
% 0.30/0.69 = { by lemma 18 R->L }
% 0.30/0.69 meet(join(Y, X), join(meet(join(Y, X), X), meet(Y, join(Y, X))))
% 0.30/0.69 = { by lemma 18 R->L }
% 0.30/0.69 meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X))
% 0.30/0.69 = { by lemma 9 R->L }
% 0.30/0.69 join(meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)), meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)))
% 0.30/0.69 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.30/0.69 join(meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)), meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X))))
% 0.30/0.69 = { by axiom 2 (wal_absorbtion_1) }
% 0.30/0.69 join(meet(join(Y, X), X), meet(Y, join(Y, X)))
% 0.30/0.69 = { by lemma 18 }
% 0.30/0.69 join(meet(join(Y, X), X), meet(join(Y, X), Y))
% 0.30/0.69 = { by lemma 20 }
% 0.30/0.69 join(meet(join(Y, X), X), Y)
% 0.30/0.69 = { by lemma 18 }
% 0.30/0.69 join(meet(X, join(Y, X)), Y)
% 0.30/0.69 = { by lemma 19 }
% 0.30/0.69 join(X, Y)
% 0.30/0.69
% 0.30/0.69 Goal 1 (prove_normal_axioms): tuple(join(a, a), join(b, a), meet(a, a), meet(b, a)) = tuple(a, join(a, b), a, meet(a, b)).
% 0.30/0.69 Proof:
% 0.30/0.69 tuple(join(a, a), join(b, a), meet(a, a), meet(b, a))
% 0.30/0.69 = { by lemma 7 }
% 0.30/0.69 tuple(join(a, a), join(b, a), a, meet(b, a))
% 0.30/0.69 = { by lemma 9 }
% 0.30/0.69 tuple(a, join(b, a), a, meet(b, a))
% 0.30/0.69 = { by lemma 21 R->L }
% 0.30/0.69 tuple(a, meet(join(b, a), join(a, b)), a, meet(b, a))
% 0.30/0.69 = { by lemma 21 R->L }
% 0.30/0.69 tuple(a, meet(join(b, a), meet(join(a, b), join(b, a))), a, meet(b, a))
% 0.30/0.69 = { by lemma 13 }
% 0.30/0.69 tuple(a, meet(join(a, b), join(b, a)), a, meet(b, a))
% 0.30/0.69 = { by lemma 21 }
% 0.30/0.69 tuple(a, join(a, b), a, meet(b, a))
% 0.30/0.69 = { by lemma 18 R->L }
% 0.30/0.69 tuple(a, join(a, b), a, meet(a, b))
% 0.30/0.69 % SZS output end Proof
% 0.30/0.69
% 0.30/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------