TSTP Solution File: GRP203-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP203-1 : TPTP v8.1.2. Released v2.2.0.
% 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 01:17:46 EDT 2023
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP203-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:38:28 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.20/0.55 Command-line arguments: --no-flatten-goal
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.20/0.57 Axiom 2 (left_inverse): multiply(left_inverse(X), X) = identity.
% 0.20/0.57 Axiom 3 (moufang3): multiply(multiply(multiply(X, Y), X), Z) = multiply(X, multiply(Y, multiply(X, Z))).
% 0.20/0.57
% 0.20/0.57 Lemma 4: multiply(multiply(X, identity), Y) = multiply(X, Y).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(multiply(X, identity), Y)
% 0.20/0.57 = { by axiom 1 (left_identity) R->L }
% 0.20/0.57 multiply(multiply(multiply(identity, X), identity), Y)
% 0.20/0.57 = { by axiom 3 (moufang3) }
% 0.20/0.57 multiply(identity, multiply(X, multiply(identity, Y)))
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 multiply(X, multiply(identity, Y))
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 multiply(X, Y)
% 0.20/0.57
% 0.20/0.57 Lemma 5: multiply(multiply(X, multiply(Y, multiply(X, identity))), Z) = multiply(X, multiply(Y, multiply(X, Z))).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(multiply(X, multiply(Y, multiply(X, identity))), Z)
% 0.20/0.57 = { by axiom 3 (moufang3) R->L }
% 0.20/0.57 multiply(multiply(multiply(multiply(X, Y), X), identity), Z)
% 0.20/0.57 = { by lemma 4 }
% 0.20/0.57 multiply(multiply(multiply(X, Y), X), Z)
% 0.20/0.57 = { by axiom 3 (moufang3) }
% 0.20/0.57 multiply(X, multiply(Y, multiply(X, Z)))
% 0.20/0.57
% 0.20/0.57 Lemma 6: multiply(left_inverse(X), multiply(X, multiply(left_inverse(X), Y))) = multiply(left_inverse(X), Y).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(left_inverse(X), multiply(X, multiply(left_inverse(X), Y)))
% 0.20/0.57 = { by axiom 3 (moufang3) R->L }
% 0.20/0.57 multiply(multiply(multiply(left_inverse(X), X), left_inverse(X)), Y)
% 0.20/0.57 = { by axiom 2 (left_inverse) }
% 0.20/0.57 multiply(multiply(identity, left_inverse(X)), Y)
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 multiply(left_inverse(X), Y)
% 0.20/0.57
% 0.20/0.57 Lemma 7: multiply(left_inverse(X), multiply(X, identity)) = identity.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(left_inverse(X), multiply(X, identity))
% 0.20/0.57 = { by axiom 2 (left_inverse) R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(X, multiply(left_inverse(X), X)))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 multiply(left_inverse(X), X)
% 0.20/0.57 = { by axiom 2 (left_inverse) }
% 0.20/0.57 identity
% 0.20/0.57
% 0.20/0.57 Lemma 8: multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity)) = identity.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity))
% 0.20/0.57 = { by axiom 2 (left_inverse) R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), X)))
% 0.20/0.57 = { by lemma 5 R->L }
% 0.20/0.57 multiply(multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), identity))), X)
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(multiply(left_inverse(X), identity), X)
% 0.20/0.57 = { by lemma 4 }
% 0.20/0.57 multiply(left_inverse(X), X)
% 0.20/0.57 = { by axiom 2 (left_inverse) }
% 0.20/0.57 identity
% 0.20/0.57
% 0.20/0.57 Lemma 9: multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(multiply(X, X), Y)
% 0.20/0.57 = { by lemma 4 R->L }
% 0.20/0.57 multiply(multiply(multiply(X, identity), X), Y)
% 0.20/0.57 = { by axiom 3 (moufang3) }
% 0.20/0.57 multiply(X, multiply(identity, multiply(X, Y)))
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 multiply(X, multiply(X, Y))
% 0.20/0.57
% 0.20/0.57 Lemma 10: multiply(multiply(X, multiply(Y, multiply(Y, multiply(X, identity)))), Z) = multiply(X, multiply(Y, multiply(Y, multiply(X, Z)))).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(multiply(X, multiply(Y, multiply(Y, multiply(X, identity)))), Z)
% 0.20/0.57 = { by lemma 9 R->L }
% 0.20/0.57 multiply(multiply(X, multiply(multiply(Y, Y), multiply(X, identity))), Z)
% 0.20/0.57 = { by lemma 5 }
% 0.20/0.57 multiply(X, multiply(multiply(Y, Y), multiply(X, Z)))
% 0.20/0.57 = { by lemma 9 }
% 0.20/0.57 multiply(X, multiply(Y, multiply(Y, multiply(X, Z))))
% 0.20/0.57
% 0.20/0.57 Lemma 11: multiply(X, multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y)))) = multiply(multiply(X, multiply(left_inverse(X), identity)), Y).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y))))
% 0.20/0.57 = { by lemma 10 R->L }
% 0.20/0.57 multiply(multiply(X, multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, identity)))), Y)
% 0.20/0.57 = { by lemma 7 }
% 0.20/0.57 multiply(multiply(X, multiply(left_inverse(X), identity)), Y)
% 0.20/0.57
% 0.20/0.57 Lemma 12: multiply(X, multiply(left_inverse(X), Y)) = Y.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, multiply(left_inverse(X), Y))
% 0.20/0.57 = { by axiom 1 (left_identity) R->L }
% 0.20/0.57 multiply(identity, multiply(X, multiply(left_inverse(X), Y)))
% 0.20/0.57 = { by lemma 8 R->L }
% 0.20/0.57 multiply(multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity)), multiply(X, multiply(left_inverse(X), Y)))
% 0.20/0.57 = { by lemma 11 R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), multiply(X, multiply(left_inverse(X), Y))))))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), Y))))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 multiply(multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity)), Y)
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(identity, Y)
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 Y
% 0.20/0.57
% 0.20/0.57 Lemma 13: multiply(X, identity) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, identity)
% 0.20/0.57 = { by axiom 2 (left_inverse) R->L }
% 0.20/0.57 multiply(X, multiply(left_inverse(X), X))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 14: multiply(left_inverse(X), multiply(X, Y)) = Y.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(left_inverse(X), multiply(X, Y))
% 0.20/0.57 = { by axiom 1 (left_identity) R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(X, multiply(identity, Y)))
% 0.20/0.57 = { by lemma 8 R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(X, multiply(multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity)), Y)))
% 0.20/0.57 = { by lemma 11 R->L }
% 0.20/0.57 multiply(left_inverse(X), multiply(X, multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), Y))))))
% 0.20/0.57 = { by lemma 6 }
% 0.20/0.57 multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), Y))))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 multiply(multiply(left_inverse(X), multiply(left_inverse(left_inverse(X)), identity)), Y)
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 multiply(identity, Y)
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.57 Y
% 0.20/0.57
% 0.20/0.57 Lemma 15: left_inverse(left_inverse(X)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 left_inverse(left_inverse(X))
% 0.20/0.57 = { by lemma 13 R->L }
% 0.20/0.57 multiply(left_inverse(left_inverse(X)), identity)
% 0.20/0.57 = { by axiom 2 (left_inverse) R->L }
% 0.20/0.57 multiply(left_inverse(left_inverse(X)), multiply(left_inverse(X), X))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 16: multiply(X, multiply(multiply(left_inverse(X), Y), X)) = multiply(Y, X).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(X, multiply(multiply(left_inverse(X), Y), X))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 multiply(X, multiply(multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y))), X))
% 0.20/0.57 = { by lemma 13 R->L }
% 0.20/0.57 multiply(X, multiply(multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y))), multiply(X, identity)))
% 0.20/0.57 = { by axiom 3 (moufang3) R->L }
% 0.20/0.57 multiply(multiply(multiply(X, multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y)))), X), identity)
% 0.20/0.57 = { by lemma 13 }
% 0.20/0.57 multiply(multiply(X, multiply(left_inverse(X), multiply(left_inverse(X), multiply(X, Y)))), X)
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 multiply(multiply(multiply(X, multiply(left_inverse(X), identity)), Y), X)
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 multiply(multiply(identity, Y), X)
% 0.20/0.57 = { by axiom 1 (left_identity) }
% 0.20/0.58 multiply(Y, X)
% 0.20/0.58
% 0.20/0.58 Goal 1 (prove_moufang2): multiply(multiply(multiply(a, b), c), b) = multiply(a, multiply(b, multiply(c, b))).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(multiply(multiply(a, b), c), b)
% 0.20/0.58 = { by lemma 14 R->L }
% 0.20/0.58 multiply(multiply(multiply(a, multiply(left_inverse(c), multiply(c, b))), c), b)
% 0.20/0.58 = { by lemma 12 R->L }
% 0.20/0.58 multiply(multiply(multiply(c, multiply(left_inverse(c), multiply(a, multiply(left_inverse(c), multiply(c, b))))), c), b)
% 0.20/0.58 = { by axiom 3 (moufang3) }
% 0.20/0.58 multiply(c, multiply(multiply(left_inverse(c), multiply(a, multiply(left_inverse(c), multiply(c, b)))), multiply(c, b)))
% 0.20/0.58 = { by axiom 3 (moufang3) R->L }
% 0.20/0.58 multiply(c, multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(c, b)), multiply(c, b)))
% 0.20/0.58 = { by axiom 1 (left_identity) R->L }
% 0.20/0.58 multiply(c, multiply(identity, multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(c, b)), multiply(c, b))))
% 0.20/0.58 = { by lemma 12 R->L }
% 0.20/0.58 multiply(c, multiply(multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), identity)), multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(c, b)), multiply(c, b))))
% 0.20/0.58 = { by lemma 11 R->L }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(c, b), multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(c, b)), multiply(c, b)))))))
% 0.20/0.58 = { by lemma 13 R->L }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(c, b), multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), identity)), multiply(c, b)))))))
% 0.20/0.58 = { by lemma 13 R->L }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(c, b), multiply(multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), identity)), multiply(multiply(c, b), identity)))))))
% 0.20/0.58 = { by axiom 3 (moufang3) R->L }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(multiply(multiply(c, b), multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), identity))), multiply(c, b)), identity)))))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(multiply(c, b), multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), multiply(c, b)))), identity)))))
% 0.20/0.58 = { by lemma 13 }
% 0.20/0.58 multiply(c, multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), multiply(left_inverse(multiply(c, b)), multiply(multiply(c, b), multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), multiply(c, b))))))))
% 0.20/0.58 = { by lemma 11 }
% 0.20/0.58 multiply(c, multiply(multiply(multiply(c, b), multiply(left_inverse(multiply(c, b)), identity)), multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), multiply(c, b)))))
% 0.20/0.58 = { by lemma 12 }
% 0.20/0.58 multiply(c, multiply(identity, multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), multiply(c, b)))))
% 0.20/0.58 = { by axiom 1 (left_identity) }
% 0.20/0.58 multiply(c, multiply(multiply(multiply(left_inverse(c), a), left_inverse(c)), multiply(multiply(c, b), multiply(c, b))))
% 0.20/0.58 = { by axiom 3 (moufang3) }
% 0.20/0.58 multiply(c, multiply(left_inverse(c), multiply(a, multiply(left_inverse(c), multiply(multiply(c, b), multiply(c, b))))))
% 0.20/0.58 = { by lemma 12 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(c, b), multiply(c, b))))
% 0.20/0.58 = { by lemma 15 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(c, b))))
% 0.20/0.58 = { by lemma 15 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(c, left_inverse(left_inverse(b))))))
% 0.20/0.58 = { by lemma 13 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), identity))))
% 0.20/0.58 = { by axiom 2 (left_inverse) R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), b)))))
% 0.20/0.58 = { by lemma 12 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(b, multiply(left_inverse(b), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), b)))))))
% 0.20/0.58 = { by lemma 10 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(b, multiply(multiply(left_inverse(b), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), identity)))), b))))
% 0.20/0.58 = { by lemma 16 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), identity))), b)))
% 0.20/0.58 = { by lemma 13 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, left_inverse(left_inverse(b))), left_inverse(b))), b)))
% 0.20/0.58 = { by lemma 13 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(multiply(c, multiply(left_inverse(left_inverse(b)), identity)), left_inverse(b))), b)))
% 0.20/0.58 = { by lemma 16 R->L }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), multiply(multiply(left_inverse(left_inverse(b)), multiply(c, multiply(left_inverse(left_inverse(b)), identity))), left_inverse(b)))), b)))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(left_inverse(b), multiply(left_inverse(left_inverse(b)), multiply(c, multiply(left_inverse(left_inverse(b)), left_inverse(b)))))), b)))
% 0.20/0.58 = { by lemma 12 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(c, multiply(left_inverse(left_inverse(b)), left_inverse(b)))), b)))
% 0.20/0.58 = { by axiom 2 (left_inverse) }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), multiply(c, identity)), b)))
% 0.20/0.58 = { by lemma 13 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(multiply(multiply(c, left_inverse(left_inverse(b))), c), b)))
% 0.20/0.58 = { by axiom 3 (moufang3) }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(c, multiply(left_inverse(left_inverse(b)), multiply(c, b)))))
% 0.20/0.58 = { by lemma 15 }
% 0.20/0.58 multiply(a, multiply(left_inverse(c), multiply(c, multiply(b, multiply(c, b)))))
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 multiply(a, multiply(b, multiply(c, b)))
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------